फलन (f(x)=|x-4|+1) का परिसर क्या है?
What is the range of (f(x)=|x-4|+1)?
#range
#modulus-function
#class11
A \(\mathbb{R}\)
B \([0,\infty\))
C \([1,\infty\))
D (\(-\infty,1]\)
Explanation opens after your attempt
Correct Answer
C. \([1,\infty\))
Step 1
Concept
\(|x-4|\ge 0\), so \(|x-4|+1\ge 1\). Therefore the range is \([1,\infty\)).
Step 2
Why this answer is correct
The correct answer is C. \([1,\infty\)). \(|x-4|\ge 0\), so \(|x-4|+1\ge 1\). Therefore the range is \([1,\infty\)).
Step 3
Exam Tip
\(|x-4|\ge 0\), इसलिए \(|x-4|+1\ge 1\) है। अतः परिसर \([1,\infty\)) है।
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फलन (f(x)=|x-4|+1) का न्यूनतम मान क्या है?
What is the minimum value of (f(x)=|x-4|+1)?
#modulus-function
#minimum
#class11
A (0)
B (1)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The minimum value of (|x-4|) is (0). Hence the minimum value of (|x-4|+1) is (1).
Step 2
Why this answer is correct
The correct answer is B. (1). The minimum value of (|x-4|) is (0). Hence the minimum value of (|x-4|+1) is (1).
Step 3
Exam Tip
(|x-4|) का न्यूनतम मान (0) होता है। इसलिए (|x-4|+1) का न्यूनतम मान (1) है।
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फलन (f(x)=x-2 +9) का परिसर क्या है?
What is the range of (f(x)=x-2 +9)?
#range
#quadratic-function
#class11
A \([0,\infty\))
B \([9,\infty\))
C (\(9,\infty\))
D \(\mathbb{R}\)
Explanation opens after your attempt
Correct Answer
B. \([9,\infty\))
Step 1
Concept
The minimum value of \(x^2\) is (0), so the minimum value of \(x^2+9\) is (9). Thus the range is \([9,\infty\)).
Step 2
Why this answer is correct
The correct answer is B. \([9,\infty\)). The minimum value of \(x^2\) is (0), so the minimum value of \(x^2+9\) is (9). Thus the range is \([9,\infty\)).
Step 3
Exam Tip
\(x^2\) का न्यूनतम मान (0) है, इसलिए \(x^2+9\) का न्यूनतम मान (9) है। अतः परिसर \([9,\infty\)) है।
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फलन (f(x)=\frac{x+2}{x+5}) का प्रांत क्या है?
What is the domain of (f(x)=\frac{x+2}{x+5})?
#domain
#rational-expression
#class11
A \(\mathbb{R}-{-5}\)
B \(\mathbb{R}-{5}\)
C \([ -5,\infty\))
D \(\mathbb{R}\)
Explanation opens after your attempt
Correct Answer
A. \(\mathbb{R}-{-5}\)
Step 1
Concept
The denominator is (x+5), and it becomes (0) at (x=-5). Hence (-5) is excluded from the domain.
Step 2
Why this answer is correct
The correct answer is A. \(\mathbb{R}-{-5}\). The denominator is (x+5), and it becomes (0) at (x=-5). Hence (-5) is excluded from the domain.
Step 3
Exam Tip
हर (x+5) है और (x=-5) पर यह (0) होता है। इसलिए (-5) को प्रांत से हटाते हैं।
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फलन (f(x)=\sqrt{8-x}) का वास्तविक प्रांत क्या है?
What is the real domain of (f(x)=\sqrt{8-x})?
#domain
#square-root
#class11
A \([8,\infty\))
B (\(-\infty,8\))
C (\(-\infty,8]\)
D \(\mathbb{R}-{8}\)
Explanation opens after your attempt
Correct Answer
C. (\(-\infty,8]\)
Step 1
Concept
The expression inside the square root must satisfy \(8-x \ge 0\). This gives \(x \le 8\), so the domain is (\(-\infty,8]\).
Step 2
Why this answer is correct
The correct answer is C. (\(-\infty,8]\). The expression inside the square root must satisfy \(8-x \ge 0\). This gives \(x \le 8\), so the domain is (\(-\infty,8]\).
Step 3
Exam Tip
वर्गमूल के अंदर \(8-x \ge 0\) होना चाहिए। इससे \(x \le 8\) और प्रांत (\(-\infty,8]\) मिलता है।
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फलन (f(x)=7-2x) का परिसर क्या है जब \(x \in \mathbb{R}\)?
What is the range of (f(x)=7-2x) when \(x \in \mathbb{R}\)?
#range
#linear-function
#class11
A \([7,\infty\))
B (\(-\infty,7]\)
C \(\mathbb{R}\)
D ({7})
Explanation opens after your attempt
Correct Answer
C. \(\mathbb{R}\)
Step 1
Concept
(7-2x) is a non-constant linear function and can take every real value. Therefore its range is \(\mathbb{R}\).
Step 2
Why this answer is correct
The correct answer is C. \(\mathbb{R}\). (7-2x) is a non-constant linear function and can take every real value. Therefore its range is \(\mathbb{R}\).
Step 3
Exam Tip
(7-2x) एक अस्थिर रेखीय फलन है और हर वास्तविक मान ले सकता है। इसलिए इसका परिसर \(\mathbb{R}\) है।
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यदि (f(x)=2\sqrt{x}), तो इसका परिसर क्या है?
If (f(x)=2\sqrt{x}), what is its range?
#range
#square-root
#class11
A \([0,\infty\))
B (\(0,\infty\))
C \(\mathbb{R}\)
D (\(-\infty,0]\)
Explanation opens after your attempt
Correct Answer
A. \([0,\infty\))
Step 1
Concept
\(\sqrt{x}\ge 0\), so \(2\sqrt{x}\ge 0\). At (x=0), the value is (0).
Step 2
Why this answer is correct
The correct answer is A. \([0,\infty\)). \(\sqrt{x}\ge 0\), so \(2\sqrt{x}\ge 0\). At (x=0), the value is (0).
Step 3
Exam Tip
\(\sqrt{x}\ge 0\) होता है, इसलिए \(2\sqrt{x}\ge 0\) है। (x=0) पर मान (0) मिलता है।
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यदि (f(x)=2\sqrt{x}), तो इसका वास्तविक प्रांत क्या है?
If (f(x)=2\sqrt{x}), what is its real domain?
#domain
#square-root
#class11
A \([0,\infty\))
B (\(0,\infty\))
C \(\mathbb{R}\)
D (\(-\infty,0]\)
Explanation opens after your attempt
Correct Answer
A. \([0,\infty\))
Step 1
Concept
For \(\sqrt{x}\) to be real, \(x \ge 0\) is needed. Multiplication by (2) does not change the domain.
Step 2
Why this answer is correct
The correct answer is A. \([0,\infty\)). For \(\sqrt{x}\) to be real, \(x \ge 0\) is needed. Multiplication by (2) does not change the domain.
Step 3
Exam Tip
\(\sqrt{x}\) वास्तविक होने के लिए \(x \ge 0\) चाहिए। (2) से गुणा करने पर प्रांत नहीं बदलता।
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फलन (f(x)=\frac{1}{x-2 +4}) का प्रांत क्या है?
What is the domain of (f(x)=\frac{1}{x-2 +4})?
#domain
#rational-function
#class11
A \(\mathbb{R}\)
B \(\mathbb{R}-{2}\)
C \(\mathbb{R}-{-2,2}\)
D \([0,\infty\))
Explanation opens after your attempt
Correct Answer
A. \(\mathbb{R}\)
Step 1
Concept
\(x^2+4\) is positive for every real (x). Therefore the denominator never becomes (0).
Step 2
Why this answer is correct
The correct answer is A. \(\mathbb{R}\). \(x^2+4\) is positive for every real (x). Therefore the denominator never becomes (0).
Step 3
Exam Tip
\(x^2+4\) हर वास्तविक (x) के लिए धनात्मक है। इसलिए हर कभी (0) नहीं बनता।
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फलन (f(x)=(x-1)2 ) का परिसर क्या है?
What is the range of (f(x)=(x-1)2 )?
#range
#quadratic-function
#class11
A \([0,\infty\))
B \([1,\infty\))
C \(\mathbb{R}\)
D (\(-\infty,0]\)
Explanation opens after your attempt
Correct Answer
A. \([0,\infty\))
Step 1
Concept
The square ((x-1)2 ) is always (0) or positive. At (x=1), the minimum (0) is obtained.
Step 2
Why this answer is correct
The correct answer is A. \([0,\infty\)). The square ((x-1)2 ) is always (0) or positive. At (x=1), the minimum (0) is obtained.
Step 3
Exam Tip
वर्ग ((x-1)2 ) हमेशा (0) या धनात्मक है। (x=1) पर न्यूनतम (0) मिलता है।
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यदि (f(x)=x-2 +2x+1), तो (f(1)) क्या है?
If (f(x)=x-2 +2x+1), what is (f(1))?
#function-value
#quadratic-function
#class11
A (4)
B (2)
C (1)
D (3)
Explanation opens after your attempt
Step 1
Concept
(f(1)=12 +2(1)+1=4). While substituting, evaluate each term separately.
Step 2
Why this answer is correct
The correct answer is A. (4). (f(1)=12 +2(1)+1=4). While substituting, evaluate each term separately.
Step 3
Exam Tip
(f(1)=12 +2(1)+1=4) है। प्रतिस्थापन में हर पद को अलग-अलग देखें।
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यदि (f(x)=\frac{x+1}{2}), तो (f(5)) क्या है?
If (f(x)=\frac{x+1}{2}), what is (f(5))?
#function-value
#linear-function
#class11
A (3)
B (2)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
(f(5)=\frac{5+1}{2}=3). In a fractional expression, evaluate the numerator carefully first.
Step 2
Why this answer is correct
The correct answer is A. (3). (f(5)=\frac{5+1}{2}=3). In a fractional expression, evaluate the numerator carefully first.
Step 3
Exam Tip
(f(5)=\frac{5+1}{2}=3) है। भिन्न वाले फलन में पहले कोष्ठक का मान निकालें।
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फलन (f(x)=3-|x|) का परिसर क्या है?
What is the range of (f(x)=3-|x|)?
#range
#modulus-function
#class11
A (\(-\infty,3]\)
B \([3,\infty\))
C ([0,3])
D \(\mathbb{R}\)
Explanation opens after your attempt
Correct Answer
A. (\(-\infty,3]\)
Step 1
Concept
As (|x|) becomes larger, (3-|x|) becomes smaller. The maximum is (3), and there is no lower bound.
Step 2
Why this answer is correct
The correct answer is A. (\(-\infty,3]\). As (|x|) becomes larger, (3-|x|) becomes smaller. The maximum is (3), and there is no lower bound.
Step 3
Exam Tip
(|x|) जितना बड़ा होगा, (3-|x|) उतना छोटा होगा। अधिकतम (3) है और नीचे कोई सीमा नहीं है।
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फलन (f(x)=|x|+2) का परिसर क्या है?
What is the range of (f(x)=|x|+2)?
#modulus-function
#range
#class11
A \([2,\infty\))
B \([0,\infty\))
C \(\mathbb{R}\)
D (\(-\infty,2]\)
Explanation opens after your attempt
Correct Answer
A. \([2,\infty\))
Step 1
Concept
The minimum value of (|x|) is (0). Therefore the minimum value of (|x|+2) is (2).
Step 2
Why this answer is correct
The correct answer is A. \([2,\infty\)). The minimum value of (|x|) is (0). Therefore the minimum value of (|x|+2) is (2).
Step 3
Exam Tip
(|x|) का न्यूनतम मान (0) है। इसलिए (|x|+2) का न्यूनतम मान (2) है।
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फलन (f(x)=\frac{x}{x-2}) का प्रांत क्या है?
What is the domain of (f(x)=\frac{x}{x-2})?
#domain
#rational-function
#class11
A \(\mathbb{R}-{2}\)
B \(\mathbb{R}-{0}\)
C \([2,\infty\))
D \(\mathbb{R}\)
Explanation opens after your attempt
Correct Answer
A. \(\mathbb{R}-{2}\)
Step 1
Concept
The denominator is (x-2), and it becomes (0) at (x=2). Therefore (2) is excluded.
Step 2
Why this answer is correct
The correct answer is A. \(\mathbb{R}-{2}\). The denominator is (x-2), and it becomes (0) at (x=2). Therefore (2) is excluded.
Step 3
Exam Tip
हर (x-2) है और (x=2) पर हर (0) हो जाता है। इसलिए (2) को हटाते हैं।
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यदि (f(x)=x-2 ) और \(x \in {-2,2}\), तो कितने अलग-अलग मान मिलते हैं?
If (f(x)=x-2 ) and \(x \in {-2,2}\), how many distinct values are obtained?
#range
#distinct-values
#class11
A (1)
B (2)
C (3)
D (0)
Explanation opens after your attempt
Step 1
Concept
((-2)2 =4) and \(2^2=4\), so only one distinct value is obtained. Repeated values are written once in the range.
Step 2
Why this answer is correct
The correct answer is A. (1). ((-2)2 =4) and \(2^2=4\), so only one distinct value is obtained. Repeated values are written once in the range.
Step 3
Exam Tip
((-2)2 =4) और \(2^2=4\), इसलिए केवल एक अलग मान मिलता है। परिसर में दोहराए गए मान एक बार लिखते हैं।
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फलन \(f:A\to\mathbb{R}\) में (A) किसे दर्शाता है?
In the function \(f:A\to\mathbb{R}\), what does (A) represent?
#domain
#notation
#class11
A प्रांत / Domain
B परिसर / Range
C सहप्रांत / Codomain
D केवल एक मान / Only one value
Explanation opens after your attempt
Correct Answer
A. प्रांत / Domain
Step 1
Concept
In \(f:A\to\mathbb{R}\), (A) is the input set. Hence (A) is called the domain.
Step 2
Why this answer is correct
The correct answer is A. प्रांत / Domain. In \(f:A\to\mathbb{R}\), (A) is the input set. Hence (A) is called the domain.
Step 3
Exam Tip
\(f:A\to\mathbb{R}\) में (A) इनपुट समुच्चय है। इसलिए (A) प्रांत कहलाता है।
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वास्तविक मान वाले फलन का अर्थ क्या है?
What does a real valued function mean?
#real-valued-functions
#definition
#class11
A जिसका हर मान \(\mathbb{R}\) में हो / Its every value lies in \(\mathbb{R}\)
B जिसका प्रांत खाली हो / Its domain is empty
C जो केवल (0) देता हो / It gives only (0)
D जिसमें केवल प्राकृतिक संख्याएँ हों / It contains only natural numbers
Explanation opens after your attempt
Correct Answer
A. जिसका हर मान \(\mathbb{R}\) में हो / Its every value lies in \(\mathbb{R}\)
Step 1
Concept
A real valued function has output values in the real numbers. The key focus is on the codomain or values.
Step 2
Why this answer is correct
The correct answer is A. जिसका हर मान \(\mathbb{R}\) में हो / Its every value lies in \(\mathbb{R}\). A real valued function has output values in the real numbers. The key focus is on the codomain or values.
Step 3
Exam Tip
वास्तविक मान वाला फलन वह है जिसके निर्गत मान वास्तविक संख्याएँ होते हैं। यहाँ मुख्य ध्यान सहप्रांत या मानों पर होता है।
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फलन (f(x)=\sqrt{x-2 }) किसके बराबर है?
The function (f(x)=\sqrt{x-2 }) is equal to what?
#modulus-function
#common-mistake
#class11
A (|x|)
B (x)
C (-x)
D \(x^2\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{x^2}\) is always non-negative, so it equals (|x|). A common mistake is writing it directly as (x).
Step 2
Why this answer is correct
The correct answer is A. (|x|). \(\sqrt{x^2}\) is always non-negative, so it equals (|x|). A common mistake is writing it directly as (x).
Step 3
Exam Tip
\(\sqrt{x^2}\) का मान हमेशा गैर-ऋणात्मक होता है, इसलिए यह (|x|) के बराबर है। सामान्य गलती इसे सीधे (x) लिखना है।
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फलन (f(x)=x-2 +4) का परिसर क्या है?
What is the range of (f(x)=x-2 +4)?
#range
#quadratic-function
#class11
A \([4,\infty\))
B \([0,\infty\))
C (\(4,\infty\))
D \(\mathbb{R}\)
Explanation opens after your attempt
Correct Answer
A. \([4,\infty\))
Step 1
Concept
Since \(x^2 \ge 0\), \(x^2+4 \ge 4\). Hence the range is \([4,\infty\)).
Step 2
Why this answer is correct
The correct answer is A. \([4,\infty\)). Since \(x^2 \ge 0\), \(x^2+4 \ge 4\). Hence the range is \([4,\infty\)).
Step 3
Exam Tip
क्योंकि \(x^2 \ge 0\), इसलिए \(x^2+4 \ge 4\) है। अतः परिसर \([4,\infty\)) है।
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फलन (f(x)=\frac{1}{x-2 }) का परिसर क्या है?
What is the range of (f(x)=\frac{1}{x-2 })?
#range
#rational-function
#class11
A (\(0,\infty\))
B \([0,\infty\))
C \(\mathbb{R}\)
D (\(-\infty,0\))
Explanation opens after your attempt
Correct Answer
A. (\(0,\infty\))
Step 1
Concept
When \(x \ne 0\), \(x^2>0\), so \(\frac{1}{x^2}>0\). The value (0) is never obtained.
Step 2
Why this answer is correct
The correct answer is A. (\(0,\infty\)). When \(x \ne 0\), \(x^2>0\), so \(\frac{1}{x^2}>0\). The value (0) is never obtained.
Step 3
Exam Tip
\(x \ne 0\) होने पर \(x^2>0\), इसलिए \(\frac{1}{x^2}>0\) है। मान (0) कभी नहीं मिलता।
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फलन (f(x)=\frac{1}{x-2 }) का प्रांत क्या है?
What is the domain of (f(x)=\frac{1}{x-2 })?
#domain
#rational-function
#class11
A \(\mathbb{R}-{0}\)
B \(\mathbb{R}\)
C (\(0,\infty\))
D \([0,\infty\))
Explanation opens after your attempt
Correct Answer
A. \(\mathbb{R}-{0}\)
Step 1
Concept
The denominator is \(x^2\), and it becomes (0) at (x=0). Therefore (0) is not in the domain.
Step 2
Why this answer is correct
The correct answer is A. \(\mathbb{R}-{0}\). The denominator is \(x^2\), and it becomes (0) at (x=0). Therefore (0) is not in the domain.
Step 3
Exam Tip
हर \(x^2\) है और (x=0) पर यह (0) बनता है। इसलिए (0) प्रांत में नहीं होगा।
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फलन (f(x)=x-2 -4) का परिसर क्या है?
What is the range of (f(x)=x-2 -4)?
#range
#quadratic-function
#class11
A \([-4,\infty\))
B \([0,\infty\))
C (\(-\infty,-4]\)
D \(\mathbb{R}\)
Explanation opens after your attempt
Correct Answer
A. \([-4,\infty\))
Step 1
Concept
The minimum value of \(x^2\) is (0), so the minimum value of \(x^2-4\) is (-4). Hence the range is \([-4,\infty\)).
Step 2
Why this answer is correct
The correct answer is A. \([-4,\infty\)). The minimum value of \(x^2\) is (0), so the minimum value of \(x^2-4\) is (-4). Hence the range is \([-4,\infty\)).
Step 3
Exam Tip
\(x^2\) का न्यूनतम मान (0) है, इसलिए \(x^2-4\) का न्यूनतम मान (-4) है। अतः परिसर \([-4,\infty\)) है।
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फलन (f(x)=\frac{2}{x+1}) का प्रांत क्या है?
What is the domain of (f(x)=\frac{2}{x+1})?
#domain
#rational-function
#class11
A \(\mathbb{R}-{-1}\)
B \(\mathbb{R}-{1}\)
C \([ -1,\infty\))
D \(\mathbb{R}\)
Explanation opens after your attempt
Correct Answer
A. \(\mathbb{R}-{-1}\)
Step 1
Concept
The denominator is (x+1), so it becomes (0) at (x=-1). This value is removed from the domain.
Step 2
Why this answer is correct
The correct answer is A. \(\mathbb{R}-{-1}\). The denominator is (x+1), so it becomes (0) at (x=-1). This value is removed from the domain.
Step 3
Exam Tip
हर (x+1) है, इसलिए (x=-1) पर हर (0) हो जाता है। इस मान को प्रांत से हटाते हैं।
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यदि (f(x)=4-x), तो (f(0)) क्या है?
If (f(x)=4-x), what is (f(0))?
#function-value
#linear-function
#class11
A (4)
B (0)
C (-4)
D (1)
Explanation opens after your attempt
Step 1
Concept
(f(0)=4-0=4). Substitute the given (x) directly to find the function value.
Step 2
Why this answer is correct
The correct answer is A. (4). (f(0)=4-0=4). Substitute the given (x) directly to find the function value.
Step 3
Exam Tip
(f(0)=4-0=4) है। फलन का मान निकालने में दिए गए (x) को सीधे रखें।
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फलन (f(x)=|x-2|) का परिसर क्या है?
What is the range of (f(x)=|x-2|)?
#range
#modulus-function
#class11
A \([0,\infty\))
B \([2,\infty\))
C \(\mathbb{R}\)
D (\(-\infty,0]\)
Explanation opens after your attempt
Correct Answer
A. \([0,\infty\))
Step 1
Concept
A modulus value is (0) or positive. At (x=2), the minimum (0) is obtained.
Step 2
Why this answer is correct
The correct answer is A. \([0,\infty\)). A modulus value is (0) or positive. At (x=2), the minimum (0) is obtained.
Step 3
Exam Tip
मॉड्यूलस का मान (0) या धनात्मक होता है। (x=2) पर न्यूनतम (0) मिलता है।
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फलन (f(x)=\sqrt{x+3}) का प्रांत क्या है?
What is the domain of (f(x)=\sqrt{x+3})?
#domain
#square-root
#class11
A \([-3,\infty\))
B (\(-\infty,-3]\)
C (\(-3,\infty\))
D \(\mathbb{R}\)
Explanation opens after your attempt
Correct Answer
A. \([-3,\infty\))
Step 1
Concept
The expression inside the square root must satisfy \(x+3 \ge 0\). Therefore \(x \ge -3\).
Step 2
Why this answer is correct
The correct answer is A. \([-3,\infty\)). The expression inside the square root must satisfy \(x+3 \ge 0\). Therefore \(x \ge -3\).
Step 3
Exam Tip
वर्गमूल के अंदर \(x+3 \ge 0\) होना चाहिए। इसलिए \(x \ge -3\) है।
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फलन (f(x)=\frac{1}{x-2 +1}) का वास्तविक प्रांत क्या है?
What is the real domain of (f(x)=\frac{1}{x-2 +1})?
#rational-function
#domain
#class11
A \(\mathbb{R}\)
B \(\mathbb{R}-{0}\)
C \([0,\infty\))
D ((-1,1))
Explanation opens after your attempt
Correct Answer
A. \(\mathbb{R}\)
Step 1
Concept
\(x^2+1\) is never (0). Therefore the function is defined for every real (x).
Step 2
Why this answer is correct
The correct answer is A. \(\mathbb{R}\). \(x^2+1\) is never (0). Therefore the function is defined for every real (x).
Step 3
Exam Tip
\(x^2+1\) कभी (0) नहीं होता। इसलिए फलन हर वास्तविक (x) पर परिभाषित है।
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यदि (f(x)=x+1) और प्रांत \(A=\{1,2,3\}\) है, तो परिसर क्या है?
If (f(x)=x+1) and the domain is \(A=\{1,2,3\}\), what is the range?
#finite-domain
#range
#class11
A ({2,3,4})
B ({1,2,3})
C ({0,1,2})
D ({3,4,5})
Explanation opens after your attempt
Correct Answer
A. ({2,3,4})
Step 1
Concept
Substituting (1,2,3) gives (2,3,4). For a finite domain, apply the function to each element.
Step 2
Why this answer is correct
The correct answer is A. ({2,3,4}). Substituting (1,2,3) gives (2,3,4). For a finite domain, apply the function to each element.
Step 3
Exam Tip
(1,2,3) रखने पर मान (2,3,4) मिलते हैं। सीमित प्रांत में हर तत्व पर फलन लगाएँ।
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फलन (f(x)=x-3 ) का प्रांत और परिसर क्या है?
What are the domain and range of (f(x)=x-3 )?
#cubic-function
#domain-range
#class11
A प्रांत \(\mathbb{R}\), परिसर \(\mathbb{R}\) / Domain \(\mathbb{R}\), range \(\mathbb{R}\)
B प्रांत \([0,\infty\)), परिसर \([0,\infty\)) / Domain \([0,\infty\)), range \([0,\infty\))
C प्रांत \(\mathbb{R}-{0}\), परिसर \(\mathbb{R}\) / Domain \(\mathbb{R}-{0}\), range \(\mathbb{R}\)
D प्रांत \(\mathbb{R}\), परिसर \([0,\infty\)) / Domain \(\mathbb{R}\), range \([0,\infty\))
Explanation opens after your attempt
Correct Answer
A. प्रांत \(\mathbb{R}\), परिसर \(\mathbb{R}\) / Domain \(\mathbb{R}\), range \(\mathbb{R}\)
Step 1
Concept
The cubic function is defined for every real (x) and can take every real value. Hence both are \(\mathbb{R}\).
Step 2
Why this answer is correct
The correct answer is A. प्रांत \(\mathbb{R}\), परिसर \(\mathbb{R}\) / Domain \(\mathbb{R}\), range \(\mathbb{R}\). The cubic function is defined for every real (x) and can take every real value. Hence both are \(\mathbb{R}\).
Step 3
Exam Tip
घन फलन हर वास्तविक (x) के लिए परिभाषित है और हर वास्तविक मान ले सकता है। इसलिए दोनों \(\mathbb{R}\) हैं।
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