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Mathematics Functions MCQ Questions for Class 12 General

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Question 221/574 Medium Mathematics Relations and Functions Functions Class 12 Level 20

यदि \(f:R\to R\), (f(x)=x^-3+5), तो (f^{-1}(x)) क्या होगा?

If \(f:R\to R\), (f(x)=x^-3+5), what is (f^{-1}(x))?

Explanation opens after your attempt

Correct Answer

A. \(\sqrt[3]{x-5}\)

Step 1

Concept

\(y=x^3+5\) लिखें। / Write \(y=x^3+5\).

Step 2

Why this answer is correct

\(x^3=y-5\), इसलिए \(x=\sqrt[3]{y-5}\)। / Then \(x^3=y-5\), so \(x=\sqrt[3]{y-5}\).

Step 3

Exam Tip

(y) को (x) से बदलने पर (f^{-1}(x)=\sqrt[3]{x-5})। / Replacing (y) by (x), (f^{-1}(x)=\sqrt[3]{x-5}).

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Question 222/574 Medium Mathematics Relations and Functions Functions Class 12 Level 20

यदि \(f:[0,\infty\)\to[1,\infty)), (f(x)=x^-2+1), तो (f^{-1}(10)) क्या होगा?

If \(f:[0,\infty\)\to[1,\infty)), (f(x)=x^-2+1), what is (f^{-1}(10))?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

(f^{-1}(10)) के लिए \(x^2+1=10\) हल करें। / To find (f^{-1}(10)), solve \(x^2+1=10\).

Step 2

Why this answer is correct

\(x^2=9\), इसलिए (x=3) या (x=-3)। / \(x^2=9\), so (x=3) or (x=-3).

Step 3

Exam Tip

प्रान्त \([0,\infty\)) है, इसलिए केवल (3) मान्य है। / Since the domain is \([0,\infty\)), only (3) is valid.

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Question 223/574 Medium Mathematics Relations and Functions Functions Class 12 Level 20

यदि \(f:R\to R\), (f(x)=x^-2+1), तो (f^{-1}({5})) क्या होगा?

If \(f:R\to R\), (f(x)=x^-2+1), what is (f^{-1}({5}))?

Explanation opens after your attempt

Correct Answer

A. ({-2,2})

Step 1

Concept

पूर्वछवि के लिए \(x^2+1=5\) हल करें। / For the preimage, solve \(x^2+1=5\).

Step 2

Why this answer is correct

इससे \(x^2=4\) मिलता है। / This gives \(x^2=4\).

Step 3

Exam Tip

इसलिए (x=2) या (x=-2), अतः पूर्वछवि ({-2,2}) है। / Hence (x=2) or (x=-2), so the preimage is ({-2,2}).

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Question 224/574 Medium Mathematics Relations and Functions Functions Class 12 Level 20

यदि (f(x)=x^-2-5x+6), तो (f(2), f(3), f(4)) में से कौन-से मान शून्य हैं?

If (f(x)=x^-2-5x+6), which of (f(2), f(3), f(4)) are zero?

Explanation opens after your attempt

Correct Answer

A. (f(2)) और (f(3))(f(2)) and (f(3))

Step 1

Concept

(f(x)=x^-2-5x+6=(x-2)(x-3))। / (f(x)=x^-2-5x+6=(x-2)(x-3)).

Step 2

Why this answer is correct

(x=2) और (x=3) पर गुणनफल शून्य होगा। / At (x=2) and (x=3), the product becomes zero.

Step 3

Exam Tip

(x=4) पर (f(4)=2), इसलिए वह शून्य नहीं है। / At (x=4), (f(4)=2), so it is not zero.

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Question 225/574 Medium Mathematics Relations and Functions Functions Class 12 Level 20

यदि \(f:R\to R\), (f(x)=|x-4|+1), तो परास क्या होगा?

If \(f:R\to R\), (f(x)=|x-4|+1), what is the range?

Explanation opens after your attempt

Correct Answer

A. \([1,\infty\))

Step 1

Concept

\(|x-4|\ge0\) हर वास्तविक (x) के लिए। / \(|x-4|\ge0\) for every real (x).

Step 2

Why this answer is correct

इसलिए \(|x-4|+1\ge1\)। / Therefore \(|x-4|+1\ge1\).

Step 3

Exam Tip

(x=4) पर न्यूनतम मान (1) मिलता है, अतः परास \([1,\infty\)) है। / At (x=4), the minimum value (1) is obtained, so the range is \([1,\infty\)).

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Question 226/574 Medium Mathematics Relations and Functions Functions Class 12 Level 20

यदि \(f:R\to R\), (f(x)=|x-4|+1), तो यह आच्छादक क्यों नहीं है?

If \(f:R\to R\), (f(x)=|x-4|+1), why is it not onto?

Explanation opens after your attempt

Correct Answer

A. क्योंकि (0) इसकी छवि नहीं हो सकताBecause (0) cannot be its image

Step 1

Concept

(|x-4|+1) का मान हमेशा (1) या उससे बड़ा होता है। / The value of (|x-4|+1) is always at least (1).

Step 2

Why this answer is correct

सहप्रान्त (R) में (0) है, लेकिन वह किसी (x) की छवि नहीं बन सकता। / The codomain (R) contains (0), but it cannot be the image of any (x).

Step 3

Exam Tip

इसलिए फलन आच्छादक नहीं है। / Therefore the function is not onto.

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Question 227/574 Medium Mathematics Relations and Functions Functions Class 12 Level 20

यदि \(f:A\to B\) उभयैक है और (B) में (8) अवयव हैं, तो (A) में कितने अवयव होंगे?

If \(f:A\to B\) is bijective and (B) has (8) elements, how many elements will (A) have?

Explanation opens after your attempt

Correct Answer

A. (8)

Step 1

Concept

उभयैक फलन में हर अवयव का ठीक एक-एक मिलान होता है। / In a bijective function, every element is matched exactly one-to-one.

Step 2

Why this answer is correct

इसलिए प्रान्त और सहप्रान्त में अवयवों की संख्या समान होती है। / Hence the domain and codomain have the same number of elements.

Step 3

Exam Tip

(B) में (8) अवयव हैं, अतः (A) में भी (8) होंगे। / Since (B) has (8) elements, (A) also has (8).

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Question 228/574 Medium Mathematics Relations and Functions Functions Class 12 Level 20

यदि \(f:A\to B\) और \(g:B\to A\) ऐसे हैं कि \(f\circ g=I_B\) और \(g\circ f=I_A\), तो (f) के बारे में सही कथन क्या है?

If \(f:A\to B\) and \(g:B\to A\) satisfy \(f\circ g=I_B\) and \(g\circ f=I_A\), what is correct about (f)?

Explanation opens after your attempt

Correct Answer

A. (f) उभयैक है और \(g=f^{-1}\)(f) is bijective and \(g=f^{-1}\)

Step 1

Concept

दोनों संयुक्त फलन पहचान फलन दे रहे हैं। / Both compositions give identity functions.

Step 2

Why this answer is correct

इसका अर्थ है कि (f) और (g) एक-दूसरे की क्रिया को पूरी तरह उलटते हैं। / This means (f) and (g) completely undo each other's action.

Step 3

Exam Tip

इसलिए (f) उभयैक है और (g), (f) का प्रतिलोम है। / Therefore (f) is bijective and (g) is the inverse of (f).

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Question 229/574 Medium Mathematics Relations and Functions Functions Class 12 Level 21

यदि \(f:R\to R\), (f(x)=4x+7), तो (f^{-1}(23)) का मान क्या होगा?

If \(f:R\to R\), (f(x)=4x+7), what is the value of (f^{-1}(23))?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

(f^{-1}(23)) का अर्थ है वह (x), जिसके लिए (f(x)=23)। / (f^{-1}(23)) means the value of (x) for which (f(x)=23).

Step 2

Why this answer is correct

(4x+7=23) से (4x=16), इसलिए (x=4)। / From (4x+7=23), we get (4x=16), so (x=4).

Step 3

Exam Tip

प्रतिलोम मान निकालते समय मूल फलन को दिए गए मान के बराबर रखकर हल करें। / To find an inverse value, equate the original function to the given value and solve.

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Question 230/574 Medium Mathematics Relations and Functions Functions Class 12 Level 21

यदि (f(x)=x^-2-4x), तो (f(x+1)-f(x)) क्या होगा?

If (f(x)=x^-2-4x), what is (f(x+1)-f(x))?

Explanation opens after your attempt

Correct Answer

A. (2x-3)

Step 1

Concept

(f(x+1)=(x+1)²-4(x+1)) लिखें। / Write (f(x+1)=(x+1)²-4(x+1)).

Step 2

Why this answer is correct

सरल करने पर \(x^2-2x-3\) मिलता है। / Simplifying gives \(x^2-2x-3\).

Step 3

Exam Tip

अब (x^-2-2x-3-\(x^2-4x\)=2x-3) होगा। / Now (x^-2-2x-3-\(x^2-4x\)=2x-3).

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Mathematics Functions MCQ Questions for Class 12 General

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Functions Practice Questions

यदि \(f:R\to R\), (f(x)=x-3+5), तो (f^{-1}(x)) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(f:[0,\infty\)\to[1,\infty)), (f(x)=x-2+1), तो (f^{-1}(10)) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(f:R\to R\), (f(x)=x-2+1), तो (f^{-1}({5})) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=x-2-5x+6), तो (f(2), f(3), f(4)) में से कौन-से मान शून्य हैं?

Concept

Why this answer is correct

Exam Tip

यदि \(f:R\to R\), (f(x)=|x-4|+1), तो परास क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(f:R\to R\), (f(x)=|x-4|+1), तो यह आच्छादक क्यों नहीं है?

Concept

Why this answer is correct

Exam Tip

यदि \(f:A\to B\) उभयैक है और (B) में (8) अवयव हैं, तो (A) में कितने अवयव होंगे?

Concept

Why this answer is correct

Exam Tip

यदि \(f:A\to B\) और \(g:B\to A\) ऐसे हैं कि \(f\circ g=I_B\) और \(g\circ f=I_A\), तो (f) के बारे में सही कथन क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(f:R\to R\), (f(x)=4x+7), तो (f^{-1}(23)) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=x-2-4x), तो (f(x+1)-f(x)) क्या होगा?

Concept

Why this answer is correct

Exam Tip

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यदि \(f:R\to R\), (f(x)=x^-3+5), तो (f^{-1}(x)) क्या होगा?

यदि \(f:[0,\infty\)\to[1,\infty)), (f(x)=x^-2+1), तो (f^{-1}(10)) क्या होगा?

यदि \(f:R\to R\), (f(x)=x^-2+1), तो (f^{-1}({5})) क्या होगा?

यदि (f(x)=x^-2-5x+6), तो (f(2), f(3), f(4)) में से कौन-से मान शून्य हैं?

यदि (f(x)=x^-2-4x), तो (f(x+1)-f(x)) क्या होगा?