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Mathematics Quiz - Class 11 Mathematics Relations And Fun...

Question 1/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2+1) और (g(x)=2x-3) हैं, तो ((f+g)(x)) क्या होगा?

If (f(x)=x^-2+1) and (g(x)=2x-3), what is ((f+g)(x))?

Explanation opens after your attempt

Correct Answer

A. \(x^2+2x-2\)

Step 1

Concept

((f+g)(x)=f(x)+g(x)=x^-2+1+2x-3=x^-2+2x-2). In exams, combine like terms carefully.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+2x-2\). ((f+g)(x)=f(x)+g(x)=x^-2+1+2x-3=x^-2+2x-2). In exams, combine like terms carefully.

Step 3

Exam Tip

((f+g)(x)=f(x)+g(x)=x^-2+1+2x-3=x^-2+2x-2)। परीक्षा में समान पदों को ध्यान से जोड़ें।

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Question 2/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=3x+5) और (g(x)=x^-2-4) हैं, तो ((g-f)(x)) ज्ञात कीजिए।

If (f(x)=3x+5) and (g(x)=x^-2-4), find ((g-f)(x)).

Explanation opens after your attempt

Correct Answer

A. \(x^2-3x-9\)

Step 1

Concept

((g-f)(x)=g(x)-f(x)=x^-2-4-(3x+5)=x^-2-3x-9). While subtracting, apply the minus sign to the whole (f(x)).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-3x-9\). ((g-f)(x)=g(x)-f(x)=x^-2-4-(3x+5)=x^-2-3x-9). While subtracting, apply the minus sign to the whole (f(x)).

Step 3

Exam Tip

((g-f)(x)=g(x)-f(x)=x^-2-4-(3x+5)=x^-2-3x-9)। घटाते समय पूरे (f(x)) पर ऋण लगाएँ।

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Question 3/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x+2) और (g(x)=x-5) हैं, तो ((fg)(x)) क्या है?

If (f(x)=x+2) and (g(x)=x-5), what is ((fg)(x))?

Explanation opens after your attempt

Correct Answer

A. \(x^2-3x-10\)

Step 1

Concept

((fg)(x)=f(x)g(x)=(x+2)(x-5)=x^-2-3x-10). After expanding, combine like terms.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-3x-10\). ((fg)(x)=f(x)g(x)=(x+2)(x-5)=x^-2-3x-10). After expanding, combine like terms.

Step 3

Exam Tip

((fg)(x)=f(x)g(x)=(x+2)(x-5)=x^-2-3x-10)। गुणा में विस्तार के बाद समान पद मिलाएँ।

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Question 4/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2-9) और (g(x)=x-3) हैं, तो \(x \neq 3\) के लिए (\left\(\frac{f}{g}\right\)(x)) क्या होगा?

If (f(x)=x^-2-9) and (g(x)=x-3), what is (\left\(\frac{f}{g}\right\)(x)) for \(x \neq 3\)?

Explanation opens after your attempt

Correct Answer

A. (x+3)

Step 1

Concept

(\left\(\frac{f}{g}\right\)(x)=\frac{x^-2-9}{x-3}=\frac{(x-3)(x+3)}{x-3}=x+3), where \(x \neq 3\). Always check that the denominator is not zero.

Step 2

Why this answer is correct

The correct answer is A. (x+3). (\left\(\frac{f}{g}\right\)(x)=\frac{x^-2-9}{x-3}=\frac{(x-3)(x+3)}{x-3}=x+3), where \(x \neq 3\). Always check that the denominator is not zero.

Step 3

Exam Tip

(\left\(\frac{f}{g}\right\)(x)=\frac{x^-2-9}{x-3}=\frac{(x-3)(x+3)}{x-3}=x+3), जहाँ \(x \neq 3\)। हर शून्य न हो, यह हमेशा जाँचें।

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Question 5/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=\frac{1}{x-2}) और (g(x)=\frac{1}{x+4}) हैं, तो ((f+g)(x)) का प्रांत क्या होगा?

If (f(x)=\frac{1}{x-2}) and (g(x)=\frac{1}{x+4}), what is the domain of ((f+g)(x))?

Explanation opens after your attempt

Correct Answer

A. \(x \in \mathbb{R}, x \neq 2, x \neq -4\)

Step 1

Concept

The denominators (x-2) and (x+4) must not be zero, so \(x \neq 2\) and \(x \neq -4\). In rational functions, check denominators first.

Step 2

Why this answer is correct

The correct answer is A. \(x \in \mathbb{R}, x \neq 2, x \neq -4\). The denominators (x-2) and (x+4) must not be zero, so \(x \neq 2\) and \(x \neq -4\). In rational functions, check denominators first.

Step 3

Exam Tip

हरों (x-2) और (x+4) को शून्य नहीं होना चाहिए, इसलिए \(x \neq 2\) और \(x \neq -4\)। परिमेय फलनों में हर पहले जाँचें।

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Question 6/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=2x^-2) और (g(x)=x+1) हैं, तो ((f-g)(-2)) का मान क्या है?

If (f(x)=2x^-2) and (g(x)=x+1), what is the value of ((f-g)(-2))?

Explanation opens after your attempt

Correct Answer

A. (9)

Step 1

Concept

((f-g)(x)=2x^-2-(x+1)), so ((f-g)(-2)=8-(-1)=9). First form the function, then substitute the value.

Step 2

Why this answer is correct

The correct answer is A. (9). ((f-g)(x)=2x^-2-(x+1)), so ((f-g)(-2)=8-(-1)=9). First form the function, then substitute the value.

Step 3

Exam Tip

((f-g)(x)=2x^-2-(x+1)), इसलिए ((f-g)(-2)=8-(-1)=9)। पहले फलन बनाकर फिर मान रखें।

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Question 7/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2+2x) और (g(x)=x^-2-2x) हैं, तो ((f+g)(3)) क्या है?

If (f(x)=x^-2+2x) and (g(x)=x^-2-2x), what is ((f+g)(3))?

Explanation opens after your attempt

Correct Answer

A. (18)

Step 1

Concept

((f+g)(x)=2x^-2), hence ((f+g)(3)=2\cdot 3²=18). Opposite terms may cancel, so simplify first.

Step 2

Why this answer is correct

The correct answer is A. (18). ((f+g)(x)=2x^-2), hence ((f+g)(3)=2\cdot 3²=18). Opposite terms may cancel, so simplify first.

Step 3

Exam Tip

((f+g)(x)=2x^-2), अतः ((f+g)(3)=2\cdot 3²=18)। विरोधी पद कट सकते हैं, इसलिए सरल रूप देखें।

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Question 8/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2-1) और (g(x)=2x+1) हैं, तो ((fg)(2)) ज्ञात करें।

If (f(x)=x^-2-1) and (g(x)=2x+1), find ((fg)(2)).

Explanation opens after your attempt

Correct Answer

A. (15)

Step 1

Concept

((fg)(2)=f(2)g(2)=(4-1)(5)=15). In a product, finding both values separately is often easier.

Step 2

Why this answer is correct

The correct answer is A. (15). ((fg)(2)=f(2)g(2)=(4-1)(5)=15). In a product, finding both values separately is often easier.

Step 3

Exam Tip

((fg)(2)=f(2)g(2)=(4-1)(5)=15)। उत्पाद में दोनों फलनों का मान अलग-अलग निकालना आसान है।

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Question 9/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=4x-1) और (g(x)=x^-2+2) हैं, तो ((g+f)(x)) और ((f+g)(x)) के बारे में सही कथन कौन-सा है?

If (f(x)=4x-1) and (g(x)=x^-2+2), which statement about ((g+f)(x)) and ((f+g)(x)) is correct?

Explanation opens after your attempt

Correct Answer

A. दोनों बराबर हैंBoth are equal

Step 1

Concept

Addition of functions is commutative, so ((f+g)(x)=(g+f)(x)). Changing order in addition does not change the value.

Step 2

Why this answer is correct

The correct answer is A. दोनों बराबर हैं / Both are equal. Addition of functions is commutative, so ((f+g)(x)=(g+f)(x)). Changing order in addition does not change the value.

Step 3

Exam Tip

फलनों का योग क्रमविनिमेय है, इसलिए ((f+g)(x)=(g+f)(x))। योग में क्रम बदलने से मान नहीं बदलता।

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Question 10/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x+6) और (g(x)=x-6) हैं, तो ((fg)(x)) का सरल रूप क्या है?

If (f(x)=x+6) and (g(x)=x-6), what is the simplified form of ((fg)(x))?

Explanation opens after your attempt

Correct Answer

A. \(x^2-36\)

Step 1

Concept

((fg)(x)=(x+6)(x-6)=x^-2-36). This follows the \(a^2-b^2\) pattern.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-36\). ((fg)(x)=(x+6)(x-6)=x^-2-36). This follows the \(a^2-b^2\) pattern.

Step 3

Exam Tip

((fg)(x)=(x+6)(x-6)=x^-2-36)। यह \(a^2-b^2\) का पैटर्न है।

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Question 11/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=\frac{x+1}{x-1}) और (g(x)=x-1) हैं, तो ((fg)(x)) का प्रांत क्या है?

If (f(x)=\frac{x+1}{x-1}) and (g(x)=x-1), what is the domain of ((fg)(x))?

Explanation opens after your attempt

Correct Answer

A. \(x \in \mathbb{R}, x \neq 1\)

Step 1

Concept

In the original (f(x)), \(x-1 \neq 0\), so \(x \neq 1\), even if simplification occurs after multiplication. Decide the domain from original expressions.

Step 2

Why this answer is correct

The correct answer is A. \(x \in \mathbb{R}, x \neq 1\). In the original (f(x)), \(x-1 \neq 0\), so \(x \neq 1\), even if simplification occurs after multiplication. Decide the domain from original expressions.

Step 3

Exam Tip

मूल (f(x)) में \(x-1 \neq 0\), इसलिए \(x \neq 1\), भले ही गुणा के बाद सरलीकरण हो। प्रांत मूल अभिव्यक्तियों से तय करें।

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Question 12/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=\frac{2}{x}) और (g(x)=x^-2) हैं, तो ((fg)(x)) क्या है और उसका प्रांत क्या है?

If (f(x)=\frac{2}{x}) and (g(x)=x^-2), what is ((fg)(x)) and its domain?

Explanation opens after your attempt

Correct Answer

A. \(2x, x \neq 0\)

Step 1

Concept

((fg)(x)=\frac{2}{x}\cdot x^-2=2x), but \(x \neq 0\) because of the original denominator. Keep original restrictions after simplification.

Step 2

Why this answer is correct

The correct answer is A. \(2x, x \neq 0\). ((fg)(x)=\frac{2}{x}\cdot x^-2=2x), but \(x \neq 0\) because of the original denominator. Keep original restrictions after simplification.

Step 3

Exam Tip

((fg)(x)=\frac{2}{x}\cdot x^-2=2x), पर मूल हर के कारण \(x \neq 0\)। सरलीकरण के बाद भी मूल प्रतिबंध रखें।

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Question 13/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2+4x+4) और (g(x)=x+2) हैं, तो \(x \neq -2\) के लिए (\left\(\frac{f}{g}\right\)(x)) क्या होगा?

If (f(x)=x^-2+4x+4) and (g(x)=x+2), what is (\left\(\frac{f}{g}\right\)(x)) for \(x \neq -2\)?

Explanation opens after your attempt

Correct Answer

A. (x+2)

Step 1

Concept

(\frac{x^-2+4x+4}{x+2}=\frac{(x+2)²}{x+2}=x+2), where \(x \neq -2\). Write the zero of the denominator separately.

Step 2

Why this answer is correct

The correct answer is A. (x+2). (\frac{x^-2+4x+4}{x+2}=\frac{(x+2)²}{x+2}=x+2), where \(x \neq -2\). Write the zero of the denominator separately.

Step 3

Exam Tip

(\frac{x^-2+4x+4}{x+2}=\frac{(x+2)²}{x+2}=x+2), जहाँ \(x \neq -2\)। हर का शून्य मान अलग से लिखें।

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Question 14/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=|x|) और (g(x)=x) हैं, तो ((f-g)(-5)) का मान क्या है?

If (f(x)=|x|) and (g(x)=x), what is the value of ((f-g)(-5))?

Explanation opens after your attempt

Correct Answer

A. (10)

Step 1

Concept

((f-g)(-5)=|-5|-(-5)=5+5=10). Absolute value is always non-negative.

Step 2

Why this answer is correct

The correct answer is A. (10). ((f-g)(-5)=|-5|-(-5)=5+5=10). Absolute value is always non-negative.

Step 3

Exam Tip

((f-g)(-5)=|-5|-(-5)=5+5=10)। निरपेक्ष मान हमेशा गैर-ऋणात्मक होता है।

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Question 15/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-3) और (g(x)=2x^-3-1) हैं, तो ((2f-g)(x)) क्या होगा?

If (f(x)=x^-3) and (g(x)=2x^-3-1), what is ((2f-g)(x))?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

((2f-g)(x)=2x^-3-\(2x^3-1\)=1). Do not forget sign changes while opening brackets.

Step 2

Why this answer is correct

The correct answer is A. (1). ((2f-g)(x)=2x^-3-\(2x^3-1\)=1). Do not forget sign changes while opening brackets.

Step 3

Exam Tip

((2f-g)(x)=2x^-3-\(2x^3-1\)=1)। कोष्ठक खोलते समय चिह्न बदलना न भूलें।

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Question 16/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2) और (g(x)=\sqrt{x}) हैं, तो ((f+g)(x)) का प्रांत क्या है?

If (f(x)=x^-2) and (g(x)=\sqrt{x}), what is the domain of ((f+g)(x))?

Explanation opens after your attempt

Correct Answer

A. \(x \geq 0\)

Step 1

Concept

\(x^2\) is defined for all real (x), but \(\sqrt{x}\) needs \(x \geq 0\). The domain of the sum is the intersection.

Step 2

Why this answer is correct

The correct answer is A. \(x \geq 0\). \(x^2\) is defined for all real (x), but \(\sqrt{x}\) needs \(x \geq 0\). The domain of the sum is the intersection.

Step 3

Exam Tip

\(x^2\) सभी वास्तविक (x) के लिए परिभाषित है, लेकिन \(\sqrt{x}\) के लिए \(x \geq 0\) चाहिए। योग का प्रांत प्रतिच्छेद है।

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Question 17/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=\frac{1}{x}) और (g(x)=\sqrt{x-2}) हैं, तो ((fg)(x)) का प्रांत क्या होगा?

If (f(x)=\frac{1}{x}) and (g(x)=\sqrt{x-2}), what is the domain of ((fg)(x))?

Explanation opens after your attempt

Correct Answer

A. \(x \geq 2\)

Step 1

Concept

\(\sqrt{x-2}\) requires \(x \geq 2\) and \(\frac{1}{x}\) requires \(x \neq 0\); the intersection is \(x \geq 2\). Identify the strongest restriction.

Step 2

Why this answer is correct

The correct answer is A. \(x \geq 2\). \(\sqrt{x-2}\) requires \(x \geq 2\) and \(\frac{1}{x}\) requires \(x \neq 0\); the intersection is \(x \geq 2\). Identify the strongest restriction.

Step 3

Exam Tip

\(\sqrt{x-2}\) के लिए \(x \geq 2\) और \(\frac{1}{x}\) के लिए \(x \neq 0\); प्रतिच्छेद \(x \geq 2\) है। सबसे कड़ा प्रतिबंध पहचानें।

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Question 18/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x-1) और (g(x)=x+1) हैं, तो (\left\(\frac{f}{g}\right\)(0)) का मान क्या है?

If (f(x)=x-1) and (g(x)=x+1), what is the value of (\left\(\frac{f}{g}\right\)(0))?

Explanation opens after your attempt

Correct Answer

A. (-1)

Step 1

Concept

(\left\(\frac{f}{g}\right\)(0)=\frac{f(0)}{g(0)}=\frac{-1}{1}=-1). In division, first check whether the denominator value is zero.

Step 2

Why this answer is correct

The correct answer is A. (-1). (\left\(\frac{f}{g}\right\)(0)=\frac{f(0)}{g(0)}=\frac{-1}{1}=-1). In division, first check whether the denominator value is zero.

Step 3

Exam Tip

(\left\(\frac{f}{g}\right\)(0)=\frac{f(0)}{g(0)}=\frac{-1}{1}=-1)। भाग में हर का मान शून्य है या नहीं, पहले देखें।

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Question 19/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2-4) और (g(x)=x^-2+4) हैं, तो ((g-f)(x)) क्या होगा?

If (f(x)=x^-2-4) and (g(x)=x^-2+4), what is ((g-f)(x))?

Explanation opens after your attempt

Correct Answer

A. (8)

Step 1

Concept

((g-f)(x)=\(x^2+4\)-\(x^2-4\)=8). The like \(x^2\) terms cancel.

Step 2

Why this answer is correct

The correct answer is A. (8). ((g-f)(x)=\(x^2+4\)-\(x^2-4\)=8). The like \(x^2\) terms cancel.

Step 3

Exam Tip

((g-f)(x)=\(x^2+4\)-\(x^2-4\)=8)। समान \(x^2\) पद कट जाते हैं।

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Question 20/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=2x+3), (g(x)=x-4) और (h(x)=x^-2) हैं, तो ((f+g-h)(x)) क्या है?

If (f(x)=2x+3), (g(x)=x-4), and (h(x)=x^-2), what is ((f+g-h)(x))?

Explanation opens after your attempt

Correct Answer

A. \(-x^2+3x-1\)

Step 1

Concept

((f+g-h)(x)=2x+3+x-4-x^-2=-x^-2+3x-1). With many functions, combine terms in order.

Step 2

Why this answer is correct

The correct answer is A. \(-x^2+3x-1\). ((f+g-h)(x)=2x+3+x-4-x^-2=-x^-2+3x-1). With many functions, combine terms in order.

Step 3

Exam Tip

((f+g-h)(x)=2x+3+x-4-x^-2=-x^-2+3x-1)। कई फलनों में पदों को क्रम से मिलाएँ।

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Question 21/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2+x) और (g(x)=x) हैं, तो \(x \neq 0\) के लिए (\left\(\frac{f}{g}\right\)(x)) क्या है?

If (f(x)=x^-2+x) and (g(x)=x), what is (\left\(\frac{f}{g}\right\)(x)) for \(x \neq 0\)?

Explanation opens after your attempt

Correct Answer

A. (x+1)

Step 1

Concept

(\frac{x^-2+x}{x}=\frac{x(x+1)}{x}=x+1), where \(x \neq 0\). Do not forget the restriction while cancelling a common factor.

Step 2

Why this answer is correct

The correct answer is A. (x+1). (\frac{x^-2+x}{x}=\frac{x(x+1)}{x}=x+1), where \(x \neq 0\). Do not forget the restriction while cancelling a common factor.

Step 3

Exam Tip

(\frac{x^-2+x}{x}=\frac{x(x+1)}{x}=x+1), जहाँ \(x \neq 0\)। साझा गुणनखंड काटते समय प्रतिबंध न भूलें।

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Question 22/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=\frac{x}{x+2}) और (g(x)=\frac{2}{x+2}) हैं, तो ((f+g)(x)) का सरल रूप क्या है?

If (f(x)=\frac{x}{x+2}) and (g(x)=\frac{2}{x+2}), what is the simplified form of ((f+g)(x))?

Explanation opens after your attempt

Correct Answer

A. (1), \(x \neq -2\)

Step 1

Concept

((f+g)(x)=\frac{x+2}{x+2}=1), but \(x+2 \neq 0\). It is important to write the domain restriction with the simplified answer.

Step 2

Why this answer is correct

The correct answer is A. (1), \(x \neq -2\). ((f+g)(x)=\frac{x+2}{x+2}=1), but \(x+2 \neq 0\). It is important to write the domain restriction with the simplified answer.

Step 3

Exam Tip

((f+g)(x)=\frac{x+2}{x+2}=1), लेकिन \(x+2 \neq 0\)। सरल उत्तर के साथ प्रांत का प्रतिबंध लिखना जरूरी है।

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Question 23/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=3) और (g(x)=x^-2-7x) हैं, तो ((fg)(x)) क्या होगा?

If (f(x)=3) and (g(x)=x^-2-7x), what is ((fg)(x))?

Explanation opens after your attempt

Correct Answer

A. \(3x^2-21x\)

Step 1

Concept

((fg)(x)=3\(x^2-7x\)=3x^-2-21x). When multiplying by a constant function, multiply every term.

Step 2

Why this answer is correct

The correct answer is A. \(3x^2-21x\). ((fg)(x)=3\(x^2-7x\)=3x^-2-21x). When multiplying by a constant function, multiply every term.

Step 3

Exam Tip

((fg)(x)=3\(x^2-7x\)=3x^-2-21x)। स्थिर फलन से गुणा करते समय हर पद पर गुणा करें।

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Question 24/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2+1) है, तो ((f+f)(x)) क्या होगा?

If (f(x)=x^-2+1), what is ((f+f)(x))?

Explanation opens after your attempt

Correct Answer

A. \(2x^2+2\)

Step 1

Concept

((f+f)(x)=2f(x)=2\(x^2+1\)=2x^-2+2). Adding the same function gives (2f(x)).

Step 2

Why this answer is correct

The correct answer is A. \(2x^2+2\). ((f+f)(x)=2f(x)=2\(x^2+1\)=2x^-2+2). Adding the same function gives (2f(x)).

Step 3

Exam Tip

((f+f)(x)=2f(x)=2\(x^2+1\)=2x^-2+2)। समान फलन जोड़ने पर (2f(x)) बनता है।

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Question 25/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x-2) है, तो ((ff)(x)) क्या है?

If (f(x)=x-2), what is ((ff)(x))?

Explanation opens after your attempt

Correct Answer

A. \(x^2-4x+4\)

Step 1

Concept

((ff)(x)=f(x)\cdot f(x)=(x-2)²=x^-2-4x+4). Do not confuse ((ff)(x)) with (f(f(x))).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-4x+4\). ((ff)(x)=f(x)\cdot f(x)=(x-2)²=x^-2-4x+4). Do not confuse ((ff)(x)) with (f(f(x))).

Step 3

Exam Tip

((ff)(x)=f(x)\cdot f(x)=(x-2)²=x^-2-4x+4)। ((ff)(x)) को (f(f(x))) न समझें।

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Question 26/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=\sin x) और (g(x)=\cos x) हैं, तो (\(f^2+g^2\)(x)) क्या होगा?

If (f(x)=\sin x) and (g(x)=\cos x), what is (\(f^2+g^2\)(x))?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

(\(f^2+g^2\)(x)=\sin^-2 x+\cos^-2 x=1). Remember the trigonometric identity.

Step 2

Why this answer is correct

The correct answer is A. (1). (\(f^2+g^2\)(x)=\sin^-2 x+\cos^-2 x=1). Remember the trigonometric identity.

Step 3

Exam Tip

(\(f^2+g^2\)(x)=\sin^-2 x+\cos^-2 x=1)। त्रिकोणमितीय पहचान याद रखें।

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Question 27/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2) और (g(x)=2x) हैं, तो ((f+g)(a)) का मान क्या है?

If (f(x)=x^-2) and (g(x)=2x), what is the value of ((f+g)(a))?

Explanation opens after your attempt

Correct Answer

A. \(a^2+2a\)

Step 1

Concept

((f+g)(a)=f(a)+g(a)=a^-2+2a). When the variable changes, replace every (x) by that value.

Step 2

Why this answer is correct

The correct answer is A. \(a^2+2a\). ((f+g)(a)=f(a)+g(a)=a^-2+2a). When the variable changes, replace every (x) by that value.

Step 3

Exam Tip

((f+g)(a)=f(a)+g(a)=a^-2+2a)। चर बदलने पर हर (x) की जगह वही मान रखें।

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Question 28/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2-2x) और (g(x)=x^-2+2x) हैं, तो ((fg)(0)) क्या है?

If (f(x)=x^-2-2x) and (g(x)=x^-2+2x), what is ((fg)(0))?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

(f(0)=0) and (g(0)=0), so ((fg)(0)=0). If one value in a product is zero, the product is zero.

Step 2

Why this answer is correct

The correct answer is A. (0). (f(0)=0) and (g(0)=0), so ((fg)(0)=0). If one value in a product is zero, the product is zero.

Step 3

Exam Tip

(f(0)=0) और (g(0)=0), इसलिए ((fg)(0)=0)। उत्पाद में कोई एक मान शून्य हो तो उत्पाद शून्य होता है।

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Question 29/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=\frac{1}{x-1}) और (g(x)=x+3) हैं, तो (\left\(\frac{g}{f}\right\)(x)) का प्रांत क्या है?

If (f(x)=\frac{1}{x-1}) and (g(x)=x+3), what is the domain of (\left\(\frac{g}{f}\right\)(x))?

Explanation opens after your attempt

Correct Answer

A. \(x \in \mathbb{R}, x \neq 1\)

Step 1

Concept

(f(x)) needs \(x \neq 1\), and (f(x)=\frac{1}{x-1}) is never zero. So the only restriction is \(x \neq 1\).

Step 2

Why this answer is correct

The correct answer is A. \(x \in \mathbb{R}, x \neq 1\). (f(x)) needs \(x \neq 1\), and (f(x)=\frac{1}{x-1}) is never zero. So the only restriction is \(x \neq 1\).

Step 3

Exam Tip

(f(x)) के लिए \(x \neq 1\) चाहिए और (f(x)=\frac{1}{x-1}) कभी शून्य नहीं होता। इसलिए केवल \(x \neq 1\) प्रतिबंध है।

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Question 30/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2-16) और (g(x)=x+4) हैं, तो \(x \neq -4\) के लिए (\left\(\frac{f}{g}\right\)(-1)) का मान क्या है?

If (f(x)=x^-2-16) and (g(x)=x+4), what is (\left\(\frac{f}{g}\right\)(-1)) for \(x \neq -4\)?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

(\left\(\frac{f}{g}\right\)(x)=\frac{(x-4)(x+4)}{x+4}=x-4), so at (x=-1) the value is (-5). Check directly as \(\frac{-15}{3}=-5\).

Step 2

Why this answer is correct

The correct answer is A. (3). (\left\(\frac{f}{g}\right\)(x)=\frac{(x-4)(x+4)}{x+4}=x-4), so at (x=-1) the value is (-5). Check directly as \(\frac{-15}{3}=-5\).

Step 3

Exam Tip

(\left\(\frac{f}{g}\right\)(x)=\frac{(x-4)(x+4)}{x+4}=x-4), इसलिए (x=-1) पर मान (-5) होना चाहिए; पर सही जाँच में \(\frac{-15}{3}=-5\)।

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Question 31/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2-16) और (g(x)=x+4) हैं, तो \(x \neq -4\) के लिए (\left\(\frac{f}{g}\right\)(-1)) का सही मान क्या है?

If (f(x)=x^-2-16) and (g(x)=x+4), what is the correct value of (\left\(\frac{f}{g}\right\)(-1)) for \(x \neq -4\)?

Explanation opens after your attempt

Correct Answer

A. (-5)

Step 1

Concept

(\frac{x^-2-16}{x+4}=\frac{(x-4)(x+4)}{x+4}=x-4), hence (-1-4=-5). Substitute carefully after simplification.

Step 2

Why this answer is correct

The correct answer is A. (-5). (\frac{x^-2-16}{x+4}=\frac{(x-4)(x+4)}{x+4}=x-4), hence (-1-4=-5). Substitute carefully after simplification.

Step 3

Exam Tip

(\frac{x^-2-16}{x+4}=\frac{(x-4)(x+4)}{x+4}=x-4), अतः (-1-4=-5)। सरलीकरण के बाद सही मान रखें।

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Question 32/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=\sqrt{9-x^-2}) और (g(x)=x+1) हैं, तो ((f+g)(x)) का प्रांत क्या है?

If (f(x)=\sqrt{9-x^-2}) and (g(x)=x+1), what is the domain of ((f+g)(x))?

Explanation opens after your attempt

Correct Answer

A. \(-3 \leq x \leq 3\)

Step 1

Concept

For the square root, \(9-x^2 \geq 0\), so \(-3 \leq x \leq 3\). The linear function gives no extra restriction.

Step 2

Why this answer is correct

The correct answer is A. \(-3 \leq x \leq 3\). For the square root, \(9-x^2 \geq 0\), so \(-3 \leq x \leq 3\). The linear function gives no extra restriction.

Step 3

Exam Tip

वर्गमूल के लिए \(9-x^2 \geq 0\), इसलिए \(-3 \leq x \leq 3\)। रैखिक फलन कोई अतिरिक्त प्रतिबंध नहीं देता।

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Question 33/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=2x-5) और (g(x)=5-2x) हैं, तो ((f+g)(x)) क्या होगा?

If (f(x)=2x-5) and (g(x)=5-2x), what is ((f+g)(x))?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

((f+g)(x)=2x-5+5-2x=0). Recognising opposite terms gives a quick solution.

Step 2

Why this answer is correct

The correct answer is A. (0). ((f+g)(x)=2x-5+5-2x=0). Recognising opposite terms gives a quick solution.

Step 3

Exam Tip

((f+g)(x)=2x-5+5-2x=0)। विपरीत पदों को पहचानना तेज समाधान देता है।

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Question 34/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2+3x+2) और (g(x)=x+1) हैं, तो \(x \neq -1\) के लिए (\left\(\frac{f}{g}\right\)(2)) क्या होगा?

If (f(x)=x^-2+3x+2) and (g(x)=x+1), what is (\left\(\frac{f}{g}\right\)(2)) for \(x \neq -1\)?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

(\frac{x^-2+3x+2}{x+1}=\frac{(x+1)(x+2)}{x+1}=x+2), so at (x=2) the value is (4). Factorisation saves time.

Step 2

Why this answer is correct

The correct answer is A. (4). (\frac{x^-2+3x+2}{x+1}=\frac{(x+1)(x+2)}{x+1}=x+2), so at (x=2) the value is (4). Factorisation saves time.

Step 3

Exam Tip

(\frac{x^-2+3x+2}{x+1}=\frac{(x+1)(x+2)}{x+1}=x+2), इसलिए (x=2) पर मान (4) है। गुणनखंड बनाकर समय बचाएँ।

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Question 35/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2) और (g(x)=x+2) हैं, तो ((f+g)(x)-(fg)(x)) का मान (x=1) पर क्या होगा?

If (f(x)=x^-2) and (g(x)=x+2), what is the value of ((f+g)(x)-(fg)(x)) at (x=1)?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

(f(1)=1) and (g(1)=3), so ((f+g)(1)-(fg)(1)=4-3=1). In such questions, find individual values first.

Step 2

Why this answer is correct

The correct answer is A. (1). (f(1)=1) and (g(1)=3), so ((f+g)(1)-(fg)(1)=4-3=1). In such questions, find individual values first.

Step 3

Exam Tip

(f(1)=1) और (g(1)=3), इसलिए ((f+g)(1)-(fg)(1)=4-3=1)। ऐसे प्रश्नों में पहले अलग-अलग मान निकालें।

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Question 36/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2+2) और (g(x)=2x) हैं, तो ((f-g)(x)=0) के हल क्या हैं?

If (f(x)=x^-2+2) and (g(x)=2x), what are the solutions of ((f-g)(x)=0)?

Explanation opens after your attempt

Correct Answer

A. कोई वास्तविक हल नहींNo real solution

Step 1

Concept

((f-g)(x)=x^-2-2x+2=(x-1)²+1), which is never (0). Completing the square quickly shows real solutions.

Step 2

Why this answer is correct

The correct answer is A. कोई वास्तविक हल नहीं / No real solution. ((f-g)(x)=x^-2-2x+2=(x-1)²+1), which is never (0). Completing the square quickly shows real solutions.

Step 3

Exam Tip

((f-g)(x)=x^-2-2x+2=(x-1)²+1), जो कभी (0) नहीं होता। वर्ग पूर्ण करने से वास्तविक हल जल्दी दिखता है।

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Question 37/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2-1) और (g(x)=x^-2+1) हैं, तो ((g-f)(x)) का परिसर क्या है?

If (f(x)=x^-2-1) and (g(x)=x^-2+1), what is the range of ((g-f)(x))?

Explanation opens after your attempt

Correct Answer

A. ({2})

Step 1

Concept

((g-f)(x)=2), so its range is only ({2}). The range of a constant function is a singleton set.

Step 2

Why this answer is correct

The correct answer is A. ({2}). ((g-f)(x)=2), so its range is only ({2}). The range of a constant function is a singleton set.

Step 3

Exam Tip

((g-f)(x)=2), इसलिए इसका परिसर केवल ({2}) है। स्थिर फलन का परिसर एक-सदस्यीय होता है।

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Question 38/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x+1) और (g(x)=x^-2) हैं, तो ((fg)(x)) का घात क्या है?

If (f(x)=x+1) and (g(x)=x^-2), what is the degree of ((fg)(x))?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

((fg)(x)=(x+1)x^-2=x^-3+x^-2), so the degree is (3). In polynomial products, check the highest power.

Step 2

Why this answer is correct

The correct answer is A. (3). ((fg)(x)=(x+1)x^-2=x^-3+x^-2), so the degree is (3). In polynomial products, check the highest power.

Step 3

Exam Tip

((fg)(x)=(x+1)x^-2=x^-3+x^-2), इसलिए घात (3) है। बहुपद गुणा में उच्चतम घात देखें।

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Question 39/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2-5x) और (g(x)=3x) हैं, तो ((f+g)(x)) के शून्यक कौन-से हैं?

If (f(x)=x^-2-5x) and (g(x)=3x), what are the zeroes of ((f+g)(x))?

Explanation opens after your attempt

Correct Answer

A. (0) और (2)(0) and (2)

Step 1

Concept

((f+g)(x)=x^-2-2x=x(x-2)), so the zeroes are (0) and (2). For zeroes, equate the function to (0).

Step 2

Why this answer is correct

The correct answer is A. (0) और (2) / (0) and (2). ((f+g)(x)=x^-2-2x=x(x-2)), so the zeroes are (0) and (2). For zeroes, equate the function to (0).

Step 3

Exam Tip

((f+g)(x)=x^-2-2x=x(x-2)), इसलिए शून्यक (0) और (2) हैं। शून्यक के लिए फलन को (0) के बराबर रखें।

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Question 40/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=\frac{x-2}{x+1}) और (g(x)=\frac{x+3}{x+1}) हैं, तो ((f-g)(x)) क्या होगा?

If (f(x)=\frac{x-2}{x+1}) and (g(x)=\frac{x+3}{x+1}), what is ((f-g)(x))?

Explanation opens after your attempt

Correct Answer

A. \(\frac{-5}{x+1}, x \neq -1\)

Step 1

Concept

With the same denominator, subtract numerators: (\frac{x-2-(x+3)}{x+1}=\frac{-5}{x+1}). Because of denominator (x+1), \(x \neq -1\).

Step 2

Why this answer is correct

The correct answer is A. \(\frac{-5}{x+1}, x \neq -1\). With the same denominator, subtract numerators: (\frac{x-2-(x+3)}{x+1}=\frac{-5}{x+1}). Because of denominator (x+1), \(x \neq -1\).

Step 3

Exam Tip

समान हर होने पर अंश घटाएँ: (\frac{x-2-(x+3)}{x+1}=\frac{-5}{x+1})। हर (x+1) के कारण \(x \neq -1\)।

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Question 41/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=2x+1) और (g(x)=x-2) हैं, तो ((3f+2g)(x)) क्या होगा?

If (f(x)=2x+1) and (g(x)=x-2), what is ((3f+2g)(x))?

Explanation opens after your attempt

Correct Answer

A. (8x-1)

Step 1

Concept

((3f+2g)(x)=3(2x+1)+2(x-2)=8x-1). Multiply the coefficient by the whole function.

Step 2

Why this answer is correct

The correct answer is A. (8x-1). ((3f+2g)(x)=3(2x+1)+2(x-2)=8x-1). Multiply the coefficient by the whole function.

Step 3

Exam Tip

((3f+2g)(x)=3(2x+1)+2(x-2)=8x-1)। गुणांक को पूरे फलन से गुणा करें।

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Question 42/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2+6x+9) और (g(x)=x+3) हैं, तो \(x \neq -3\) के लिए (\left\(\frac{f}{g}\right\)(0)) क्या है?

If (f(x)=x^-2+6x+9) and (g(x)=x+3), what is (\left\(\frac{f}{g}\right\)(0)) for \(x \neq -3\)?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

(\frac{x^-2+6x+9}{x+3}=\frac{(x+3)²}{x+3}=x+3), hence the value at (x=0) is (3). The perfect square identity is useful.

Step 2

Why this answer is correct

The correct answer is A. (3). (\frac{x^-2+6x+9}{x+3}=\frac{(x+3)²}{x+3}=x+3), hence the value at (x=0) is (3). The perfect square identity is useful.

Step 3

Exam Tip

(\frac{x^-2+6x+9}{x+3}=\frac{(x+3)²}{x+3}=x+3), अतः (x=0) पर मान (3) है। पूर्ण वर्ग पहचान उपयोगी है।

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Question 43/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=\frac{1}{\sqrt{x-1}}) और (g(x)=x) हैं, तो ((f+g)(x)) का प्रांत क्या है?

If (f(x)=\frac{1}{\sqrt{x-1}}) and (g(x)=x), what is the domain of ((f+g)(x))?

Explanation opens after your attempt

Correct Answer

A. (x>1)

Step 1

Concept

The denominator has \(\sqrt{x-1}\), so (x-1>0) is required. Hence the domain is (x>1).

Step 2

Why this answer is correct

The correct answer is A. (x>1). The denominator has \(\sqrt{x-1}\), so (x-1>0) is required. Hence the domain is (x>1).

Step 3

Exam Tip

हर में \(\sqrt{x-1}\) है, इसलिए (x-1>0) होना चाहिए। अतः प्रांत (x>1) है।

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Question 44/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2+1) और (g(x)=x^-2-1) हैं, तो ((f-g)(5)) क्या होगा?

If (f(x)=x^-2+1) and (g(x)=x^-2-1), what is ((f-g)(5))?

Explanation opens after your attempt

Correct Answer

A. (2)

Step 1

Concept

((f-g)(x)=\(x^2+1\)-\(x^2-1\)=2), so at any (x) the value is (2). Simplifying first reduces calculation.

Step 2

Why this answer is correct

The correct answer is A. (2). ((f-g)(x)=\(x^2+1\)-\(x^2-1\)=2), so at any (x) the value is (2). Simplifying first reduces calculation.

Step 3

Exam Tip

((f-g)(x)=\(x^2+1\)-\(x^2-1\)=2), इसलिए किसी भी (x) पर मान (2) है। पहले सरल करने से गणना कम होती है।

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Question 45/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=2x) और (g(x)=\frac{1}{2}x) हैं, तो ((fg)(x)) क्या है?

If (f(x)=2x) and (g(x)=\frac{1}{2}x), what is ((fg)(x))?

Explanation opens after your attempt

Correct Answer

A. \(x^2\)

Step 1

Concept

((fg)(x)=2x\cdot \frac{1}{2}x=x^-2). Multiply numerical coefficients first.

Step 2

Why this answer is correct

The correct answer is A. \(x^2\). ((fg)(x)=2x\cdot \frac{1}{2}x=x^-2). Multiply numerical coefficients first.

Step 3

Exam Tip

((fg)(x)=2x\cdot \frac{1}{2}x=x^-2)। संख्यात्मक गुणांकों को पहले गुणा करें।

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Question 46/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2+x+1) और (g(x)=x^-2-x+1) हैं, तो ((f-g)(x)) क्या है?

If (f(x)=x^-2+x+1) and (g(x)=x^-2-x+1), what is ((f-g)(x))?

Explanation opens after your attempt

Correct Answer

A. (2x)

Step 1

Concept

((f-g)(x)=x^-2+x+1-\(x^2-x+1\)=2x). Open brackets and change signs carefully.

Step 2

Why this answer is correct

The correct answer is A. (2x). ((f-g)(x)=x^-2+x+1-\(x^2-x+1\)=2x). Open brackets and change signs carefully.

Step 3

Exam Tip

((f-g)(x)=x^-2+x+1-\(x^2-x+1\)=2x)। कोष्ठक खोलकर चिह्न सावधानी से बदलें।

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Question 47/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=\frac{x+2}{x-3}) और (g(x)=x-3) हैं, तो ((fg)(4)) क्या होगा?

If (f(x)=\frac{x+2}{x-3}) and (g(x)=x-3), what is ((fg)(4))?

Explanation opens after your attempt

Correct Answer

A. (6)

Step 1

Concept

((fg)(x)=\frac{x+2}{x-3}(x-3)=x+2), where \(x \neq 3\). At (x=4), the value is (6).

Step 2

Why this answer is correct

The correct answer is A. (6). ((fg)(x)=\frac{x+2}{x-3}(x-3)=x+2), where \(x \neq 3\). At (x=4), the value is (6).

Step 3

Exam Tip

((fg)(x)=\frac{x+2}{x-3}(x-3)=x+2), जहाँ \(x \neq 3\)। (x=4) पर मान (6) है।

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Question 48/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=\sqrt{x}) और (g(x)=\sqrt{x}) हैं, तो ((fg)(x)) और उसका प्रांत क्या है?

If (f(x)=\sqrt{x}) and (g(x)=\sqrt{x}), what are ((fg)(x)) and its domain?

Explanation opens after your attempt

Correct Answer

A. \(x, x \geq 0\)

Step 1

Concept

((fg)(x)=\sqrt{x}\cdot\sqrt{x}=x), but both square roots require \(x \geq 0\). The simplified form does not change the original domain.

Step 2

Why this answer is correct

The correct answer is A. \(x, x \geq 0\). ((fg)(x)=\sqrt{x}\cdot\sqrt{x}=x), but both square roots require \(x \geq 0\). The simplified form does not change the original domain.

Step 3

Exam Tip

((fg)(x)=\sqrt{x}\cdot\sqrt{x}=x), लेकिन दोनों वर्गमूलों के लिए \(x \geq 0\)। सरल रूप से प्रांत नहीं बदलता।

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Question 49/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x^-2-3x+2) और (g(x)=x-1) हैं, तो \(x \neq 1\) के लिए (\left\(\frac{f}{g}\right\)(3)) क्या है?

If (f(x)=x^-2-3x+2) and (g(x)=x-1), what is (\left\(\frac{f}{g}\right\)(3)) for \(x \neq 1\)?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

(\frac{x^-2-3x+2}{x-1}=\frac{(x-1)(x-2)}{x-1}=x-2), so at (x=3) the value is (1). Factorisation makes division simple.

Step 2

Why this answer is correct

The correct answer is A. (1). (\frac{x^-2-3x+2}{x-1}=\frac{(x-1)(x-2)}{x-1}=x-2), so at (x=3) the value is (1). Factorisation makes division simple.

Step 3

Exam Tip

(\frac{x^-2-3x+2}{x-1}=\frac{(x-1)(x-2)}{x-1}=x-2), अतः (x=3) पर मान (1) है। गुणनखंडन से भाग सरल होता है।

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Question 50/50 Medium Mathematics Relations and Functions Algebra of real functions Class 11 Level 38

यदि (f(x)=x+4) और (g(x)=4-x) हैं, तो ((fg)(x)) किसके बराबर है?

If (f(x)=x+4) and (g(x)=4-x), what is ((fg)(x)) equal to?

Explanation opens after your attempt

Correct Answer

A. \(16-x^2\)

Step 1

Concept

((fg)(x)=(x+4)(4-x)=16-x^-2). View it as ((4+x)(4-x)).

Step 2

Why this answer is correct

The correct answer is A. \(16-x^2\). ((fg)(x)=(x+4)(4-x)=16-x^-2). View it as ((4+x)(4-x)).

Step 3

Exam Tip

((fg)(x)=(x+4)(4-x)=16-x^-2)। इसे ((4+x)(4-x)) के रूप में देखें।

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Class 11 Mathematics - Relations And Functions - Algebra of real functions Medium Quiz

यदि (f(x)=x-2+1) और (g(x)=2x-3) हैं, तो ((f+g)(x)) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=3x+5) और (g(x)=x-2-4) हैं, तो ((g-f)(x)) ज्ञात कीजिए।

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=x+2) और (g(x)=x-5) हैं, तो ((fg)(x)) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=x-2-9) और (g(x)=x-3) हैं, तो \(x \neq 3\) के लिए (\left\(\frac{f}{g}\right\)(x)) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=\frac{1}{x-2}) और (g(x)=\frac{1}{x+4}) हैं, तो ((f+g)(x)) का प्रांत क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=2x-2) और (g(x)=x+1) हैं, तो ((f-g)(-2)) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=x-2+2x) और (g(x)=x-2-2x) हैं, तो ((f+g)(3)) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=x-2-1) और (g(x)=2x+1) हैं, तो ((fg)(2)) ज्ञात करें।

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=4x-1) और (g(x)=x-2+2) हैं, तो ((g+f)(x)) और ((f+g)(x)) के बारे में सही कथन कौन-सा है?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=x+6) और (g(x)=x-6) हैं, तो ((fg)(x)) का सरल रूप क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=\frac{x+1}{x-1}) और (g(x)=x-1) हैं, तो ((fg)(x)) का प्रांत क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=\frac{2}{x}) और (g(x)=x-2) हैं, तो ((fg)(x)) क्या है और उसका प्रांत क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=x-2+4x+4) और (g(x)=x+2) हैं, तो \(x \neq -2\) के लिए (\left\(\frac{f}{g}\right\)(x)) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=|x|) और (g(x)=x) हैं, तो ((f-g)(-5)) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=x-3) और (g(x)=2x-3-1) हैं, तो ((2f-g)(x)) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=x-2) और (g(x)=\sqrt{x}) हैं, तो ((f+g)(x)) का प्रांत क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=\frac{1}{x}) और (g(x)=\sqrt{x-2}) हैं, तो ((fg)(x)) का प्रांत क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=x-1) और (g(x)=x+1) हैं, तो (\left\(\frac{f}{g}\right\)(0)) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=x-2-4) और (g(x)=x-2+4) हैं, तो ((g-f)(x)) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=2x+3), (g(x)=x-4) और (h(x)=x-2) हैं, तो ((f+g-h)(x)) क्या है?

Concept

Why this answer is correct

यदि (f(x)=x^-2+1) और (g(x)=2x-3) हैं, तो ((f+g)(x)) क्या होगा?

यदि (f(x)=3x+5) और (g(x)=x^-2-4) हैं, तो ((g-f)(x)) ज्ञात कीजिए।

यदि (f(x)=x^-2-9) और (g(x)=x-3) हैं, तो \(x \neq 3\) के लिए (\left\(\frac{f}{g}\right\)(x)) क्या होगा?

यदि (f(x)=2x^-2) और (g(x)=x+1) हैं, तो ((f-g)(-2)) का मान क्या है?

यदि (f(x)=x^-2+2x) और (g(x)=x^-2-2x) हैं, तो ((f+g)(3)) क्या है?

यदि (f(x)=x^-2-1) और (g(x)=2x+1) हैं, तो ((fg)(2)) ज्ञात करें।

यदि (f(x)=4x-1) और (g(x)=x^-2+2) हैं, तो ((g+f)(x)) और ((f+g)(x)) के बारे में सही कथन कौन-सा है?

यदि (f(x)=\frac{2}{x}) और (g(x)=x^-2) हैं, तो ((fg)(x)) क्या है और उसका प्रांत क्या है?

यदि (f(x)=x^-2+4x+4) और (g(x)=x+2) हैं, तो \(x \neq -2\) के लिए (\left\(\frac{f}{g}\right\)(x)) क्या होगा?

यदि (f(x)=x^-3) और (g(x)=2x^-3-1) हैं, तो ((2f-g)(x)) क्या होगा?

यदि (f(x)=x^-2) और (g(x)=\sqrt{x}) हैं, तो ((f+g)(x)) का प्रांत क्या है?

यदि (f(x)=x^-2-4) और (g(x)=x^-2+4) हैं, तो ((g-f)(x)) क्या होगा?

यदि (f(x)=2x+3), (g(x)=x-4) और (h(x)=x^-2) हैं, तो ((f+g-h)(x)) क्या है?

यदि (f(x)=x^-2+x) और (g(x)=x) हैं, तो \(x \neq 0\) के लिए (\left\(\frac{f}{g}\right\)(x)) क्या है?

यदि (f(x)=3) और (g(x)=x^-2-7x) हैं, तो ((fg)(x)) क्या होगा?

यदि (f(x)=x^-2+1) है, तो ((f+f)(x)) क्या होगा?

यदि (f(x)=x^-2) और (g(x)=2x) हैं, तो ((f+g)(a)) का मान क्या है?

यदि (f(x)=x^-2-2x) और (g(x)=x^-2+2x) हैं, तो ((fg)(0)) क्या है?

यदि (f(x)=x^-2-16) और (g(x)=x+4) हैं, तो \(x \neq -4\) के लिए (\left\(\frac{f}{g}\right\)(-1)) का मान क्या है?

यदि (f(x)=x^-2-16) और (g(x)=x+4) हैं, तो \(x \neq -4\) के लिए (\left\(\frac{f}{g}\right\)(-1)) का सही मान क्या है?

यदि (f(x)=\sqrt{9-x^-2}) और (g(x)=x+1) हैं, तो ((f+g)(x)) का प्रांत क्या है?

यदि (f(x)=x^-2+3x+2) और (g(x)=x+1) हैं, तो \(x \neq -1\) के लिए (\left\(\frac{f}{g}\right\)(2)) क्या होगा?

यदि (f(x)=x^-2) और (g(x)=x+2) हैं, तो ((f+g)(x)-(fg)(x)) का मान (x=1) पर क्या होगा?

यदि (f(x)=x^-2+2) और (g(x)=2x) हैं, तो ((f-g)(x)=0) के हल क्या हैं?

यदि (f(x)=x^-2-1) और (g(x)=x^-2+1) हैं, तो ((g-f)(x)) का परिसर क्या है?

यदि (f(x)=x+1) और (g(x)=x^-2) हैं, तो ((fg)(x)) का घात क्या है?