यदि (f(x)=x+3) एक वास्तविक मान वाला फलन है, तो इसका प्रांत क्या है?
If (f(x)=x+3) is a real valued function, what is its domain?
#real-valued-functions
#domain-range
#class11
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A सभी वास्तविक संख्याएँ / All real numbers
B केवल धनात्मक वास्तविक संख्याएँ / Only positive real numbers
C केवल पूर्ण संख्याएँ / Only whole numbers
D केवल प्राकृतिक संख्याएँ / Only natural numbers
Explanation opens after your attempt
Correct Answer
A. सभी वास्तविक संख्याएँ / All real numbers
Step 1
Concept
The linear function (f(x)=x+3) is defined for every real (x). In exams, the domain of a basic linear function is usually \(\mathbb{R}\).
Step 2
Why this answer is correct
The correct answer is A. सभी वास्तविक संख्याएँ / All real numbers. The linear function (f(x)=x+3) is defined for every real (x). In exams, the domain of a basic linear function is usually \(\mathbb{R}\).
Step 3
Exam Tip
रेखीय फलन (f(x)=x+3) हर वास्तविक (x) के लिए परिभाषित है। परीक्षा में हर रेखीय फलन का प्रांत सामान्यतः \(\mathbb{R}\) लें।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=x-2 ) का परिसर क्या है जब प्रांत \(\mathbb{R}\) है?
What is the range of (f(x)=x-2 ) when the domain is \(\mathbb{R}\)?
#real-valued-functions
#range
#square-function
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \([0,\infty\))
B (\(-\infty,0]\)
C \(\mathbb{R}\)
D (\(0,\infty\))
Explanation opens after your attempt
Correct Answer
A. \([0,\infty\))
Step 1
Concept
For every real (x), \(x^2 \ge 0\). So the least value is (0), and the range is \([0,\infty\)).
Step 2
Why this answer is correct
The correct answer is A. \([0,\infty\)). For every real (x), \(x^2 \ge 0\). So the least value is (0), and the range is \([0,\infty\)).
Step 3
Exam Tip
किसी भी वास्तविक (x) के लिए \(x^2 \ge 0\) होता है। इसलिए सबसे छोटा मान (0) है और परिसर \([0,\infty\)) है।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=\sqrt{x}) का वास्तविक प्रांत क्या है?
What is the real domain of (f(x)=\sqrt{x})?
#domain
#square-root
#class11
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \([0,\infty\))
B (\(-\infty,0\))
C \(\mathbb{R}\)
D ((0,1))
Explanation opens after your attempt
Correct Answer
A. \([0,\infty\))
Step 1
Concept
For the square root to be real, \(x \ge 0\) is required. Hence the domain is \([0,\infty\)).
Step 2
Why this answer is correct
The correct answer is A. \([0,\infty\)). For the square root to be real, \(x \ge 0\) is required. Hence the domain is \([0,\infty\)).
Step 3
Exam Tip
वर्गमूल वास्तविक होने के लिए \(x \ge 0\) चाहिए। इसलिए प्रांत \([0,\infty\)) है।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=\frac{1}{x}) का प्रांत क्या है?
What is the domain of (f(x)=\frac{1}{x})?
#domain
#rational-function
#class11
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\mathbb{R}-{0}\)
B \(\mathbb{R}\)
C \([0,\infty\))
D (\(-\infty,0]\)
Explanation opens after your attempt
Correct Answer
A. \(\mathbb{R}-{0}\)
Step 1
Concept
The denominator is (x), so the function is not defined at (x=0). In exams, make sure the denominator is not (0).
Step 2
Why this answer is correct
The correct answer is A. \(\mathbb{R}-{0}\). The denominator is (x), so the function is not defined at (x=0). In exams, make sure the denominator is not (0).
Step 3
Exam Tip
हर में (x) है, इसलिए (x=0) पर फलन परिभाषित नहीं है। परीक्षा में हर को (0) न बनने दें।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=5) का परिसर क्या है?
What is the range of (f(x)=5)?
#constant-function
#range
#class11
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ({5})
B \(\mathbb{R}\)
C \([5,\infty\))
D (\(-\infty,5]\)
Explanation opens after your attempt
Step 1
Concept
This is a constant function and gives only the value (5). The range of a constant function is a singleton set.
Step 2
Why this answer is correct
The correct answer is A. ({5}). This is a constant function and gives only the value (5). The range of a constant function is a singleton set.
Step 3
Exam Tip
यह स्थिर फलन है और हर (x) पर मान (5) ही देता है। स्थिर फलन का परिसर एकल समुच्चय होता है।
Login to save your score, XP, coins and progress. Login
यदि (f(x)=2x-1), तो (f(3)) का मान क्या है?
If (f(x)=2x-1), what is the value of (f(3))?
#function-value
#real-valued-functions
#class11
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (5)
B (6)
C (7)
D (4)
Explanation opens after your attempt
Step 1
Concept
(f(3)=2(3)-1=5). To evaluate a function, substitute the given value in place of (x).
Step 2
Why this answer is correct
The correct answer is A. (5). (f(3)=2(3)-1=5). To evaluate a function, substitute the given value in place of (x).
Step 3
Exam Tip
(f(3)=2(3)-1=5) है। मान निकालते समय (x) की जगह दिए गए मान को रखें।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=\sqrt{x-2}) का वास्तविक प्रांत क्या है?
What is the real domain of (f(x)=\sqrt{x-2})?
#domain
#square-root
#inequality
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \([2,\infty\))
B (\(2,\infty\))
C (\(-\infty,2]\)
D \(\mathbb{R}\)
Explanation opens after your attempt
Correct Answer
A. \([2,\infty\))
Step 1
Concept
The expression inside the square root must satisfy \(x-2 \ge 0\). Thus \(x \ge 2\), so the domain is \([2,\infty\)).
Step 2
Why this answer is correct
The correct answer is A. \([2,\infty\)). The expression inside the square root must satisfy \(x-2 \ge 0\). Thus \(x \ge 2\), so the domain is \([2,\infty\)).
Step 3
Exam Tip
वर्गमूल के अंदर \(x-2 \ge 0\) होना चाहिए। इसलिए \(x \ge 2\) और प्रांत \([2,\infty\)) है।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=x-2 +1) का परिसर क्या है जब \(x \in \mathbb{R}\)?
What is the range of (f(x)=x-2 +1) when \(x \in \mathbb{R}\)?
#range
#quadratic-function
#class11
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \([1,\infty\))
B \([0,\infty\))
C \(\mathbb{R}\)
D (\(1,\infty\))
Explanation opens after your attempt
Correct Answer
A. \([1,\infty\))
Step 1
Concept
Since \(x^2 \ge 0\), we have \(x^2+1 \ge 1\). The minimum value is (1).
Step 2
Why this answer is correct
The correct answer is A. \([1,\infty\)). Since \(x^2 \ge 0\), we have \(x^2+1 \ge 1\). The minimum value is (1).
Step 3
Exam Tip
क्योंकि \(x^2 \ge 0\), इसलिए \(x^2+1 \ge 1\) है। न्यूनतम मान (1) पर मिलता है।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=|x|) का परिसर क्या है?
What is the range of (f(x)=|x|)?
#modulus-function
#range
#class11
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \([0,\infty\))
B (\(-\infty,0]\)
C \(\mathbb{R}\)
D (\(0,\infty\))
Explanation opens after your attempt
Correct Answer
A. \([0,\infty\))
Step 1
Concept
(|x|) is never negative. Therefore its range is \([0,\infty\)).
Step 2
Why this answer is correct
The correct answer is A. \([0,\infty\)). (|x|) is never negative. Therefore its range is \([0,\infty\)).
Step 3
Exam Tip
(|x|) कभी ऋणात्मक नहीं होता। इसलिए इसका परिसर \([0,\infty\)) है।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=\frac{1}{x-4}) का प्रांत क्या है?
What is the domain of (f(x)=\frac{1}{x-4})?
#domain
#rational-function
#class11
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(\mathbb{R}-{4}\)
B \(\mathbb{R}-{0}\)
C \([4,\infty\))
D (\(-\infty,4]\)
Explanation opens after your attempt
Correct Answer
A. \(\mathbb{R}-{4}\)
Step 1
Concept
The denominator is (x-4), so at (x=4) it becomes (0). Hence (4) is excluded from the domain.
Step 2
Why this answer is correct
The correct answer is A. \(\mathbb{R}-{4}\). The denominator is (x-4), so at (x=4) it becomes (0). Hence (4) is excluded from the domain.
Step 3
Exam Tip
हर (x-4) है, इसलिए (x=4) पर हर (0) बनता है। इसीलिए (4) को प्रांत से हटाते हैं।
Login to save your score, XP, coins and progress. Login
यदि \(f:\mathbb{R}\to\mathbb{R}\) और (f(x)=3x), तो (f(-2)) क्या होगा?
If \(f:\mathbb{R}\to\mathbb{R}\) and (f(x)=3x), what is (f(-2))?
#function-value
#linear-function
#class11
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (-6)
B (6)
C (-5)
D (1)
Explanation opens after your attempt
Step 1
Concept
(f(-2)=3(-2)=-6). Be careful with signs while substituting negative values.
Step 2
Why this answer is correct
The correct answer is A. (-6). (f(-2)=3(-2)=-6). Be careful with signs while substituting negative values.
Step 3
Exam Tip
(f(-2)=3(-2)=-6) है। ऋणात्मक मान रखते समय चिन्ह पर ध्यान दें।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=\sqrt{5-x}) का वास्तविक प्रांत क्या है?
What is the real domain of (f(x)=\sqrt{5-x})?
#domain
#square-root
#inequality
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (\(-\infty,5]\)
B \([5,\infty\))
C (\(-\infty,5\))
D \(\mathbb{R}\)
Explanation opens after your attempt
Correct Answer
A. (\(-\infty,5]\)
Step 1
Concept
For the square root, \(5-x \ge 0\) is needed. This gives \(x \le 5\).
Step 2
Why this answer is correct
The correct answer is A. (\(-\infty,5]\). For the square root, \(5-x \ge 0\) is needed. This gives \(x \le 5\).
Step 3
Exam Tip
वर्गमूल के लिए \(5-x \ge 0\) चाहिए। इससे \(x \le 5\) मिलता है।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=2x-2 ) का परिसर क्या है जब \(x \in \mathbb{R}\)?
What is the range of (f(x)=2x-2 ) when \(x \in \mathbb{R}\)?
#range
#quadratic-function
#class11
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \([0,\infty\))
B (\(0,\infty\))
C (\(-\infty,0]\)
D \(\mathbb{R}\)
Explanation opens after your attempt
Correct Answer
A. \([0,\infty\))
Step 1
Concept
Since \(x^2 \ge 0\), \(2x^2 \ge 0\). At (x=0), the value is (0).
Step 2
Why this answer is correct
The correct answer is A. \([0,\infty\)). Since \(x^2 \ge 0\), \(2x^2 \ge 0\). At (x=0), the value is (0).
Step 3
Exam Tip
\(x^2 \ge 0\) होने से \(2x^2 \ge 0\) है। (x=0) पर मान (0) मिलता है।
Login to save your score, XP, coins and progress. Login
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
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
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
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
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
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=\sqrt{x+3}) का प्रांत क्या है?
What is the domain of (f(x)=\sqrt{x+3})?
#domain
#square-root
#class11
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=|x-2|) का न्यूनतम मान क्या है?
What is the minimum value of (f(x)=|x-2|)?
#modulus-function
#minimum
#range
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (0)
B (1)
C (2)
D (-2)
Explanation opens after your attempt
Step 1
Concept
(|x-2|) is never negative and becomes (0) at (x=2). Hence the minimum value is (0).
Step 2
Why this answer is correct
The correct answer is A. (0). (|x-2|) is never negative and becomes (0) at (x=2). Hence the minimum value is (0).
Step 3
Exam Tip
(|x-2|) का मान कभी ऋणात्मक नहीं होता और (x=2) पर (0) हो जाता है। इसलिए न्यूनतम मान (0) है।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=|x-2|) का परिसर क्या है?
What is the range of (f(x)=|x-2|)?
#range
#modulus-function
#class11
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
यदि (f(x)=4-x), तो (f(0)) क्या है?
If (f(x)=4-x), what is (f(0))?
#function-value
#linear-function
#class11
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
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
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=\sqrt{9-x-2 }) के वास्तविक प्रांत के लिए सही शर्त कौन सी है?
Which condition is correct for the real domain of (f(x)=\sqrt{9-x-2 })?
#domain
#square-root
#interval
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(-3 \le x \le 3\)
B \(x \ge 3\)
C \(x \le -3\)
D \(x \ne 0\)
Explanation opens after your attempt
Correct Answer
A. \(-3 \le x \le 3\)
Step 1
Concept
For the square root, \(9-x^2 \ge 0\) is needed. This gives \(x^2 \le 9\), that is \(-3 \le x \le 3\).
Step 2
Why this answer is correct
The correct answer is A. \(-3 \le x \le 3\). For the square root, \(9-x^2 \ge 0\) is needed. This gives \(x^2 \le 9\), that is \(-3 \le x \le 3\).
Step 3
Exam Tip
वर्गमूल के लिए \(9-x^2 \ge 0\) चाहिए। इससे \(x^2 \le 9\), यानी \(-3 \le x \le 3\) मिलता है।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=\sqrt{9-x-2 }) का वास्तविक प्रांत कौन सा है?
What is the real domain of (f(x)=\sqrt{9-x-2 })?
#domain
#interval
#square-root
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ([-3,3])
B ((-3,3))
C (\(-\infty,-3]\cup[3,\infty\))
D \(\mathbb{R}\)
Explanation opens after your attempt
Correct Answer
A. ([-3,3])
Step 1
Concept
The condition \(9-x^2 \ge 0\) gives ([-3,3]). Include the endpoints because the square root can be (0).
Step 2
Why this answer is correct
The correct answer is A. ([-3,3]). The condition \(9-x^2 \ge 0\) gives ([-3,3]). Include the endpoints because the square root can be (0).
Step 3
Exam Tip
शर्त \(9-x^2 \ge 0\) से ([-3,3]) मिलता है। सिरों को शामिल करें क्योंकि वर्गमूल (0) हो सकता है।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=x-2 -4) का न्यूनतम मान क्या है जब \(x \in \mathbb{R}\)?
What is the minimum value of (f(x)=x-2 -4) when \(x \in \mathbb{R}\)?
#quadratic-function
#minimum
#range
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (-4)
B (0)
C (4)
D (-2)
Explanation opens after your attempt
Step 1
Concept
Since \(x^2 \ge 0\), \(x^2-4 \ge -4\). The minimum value is (-4) at (x=0).
Step 2
Why this answer is correct
The correct answer is A. (-4). Since \(x^2 \ge 0\), \(x^2-4 \ge -4\). The minimum value is (-4) at (x=0).
Step 3
Exam Tip
क्योंकि \(x^2 \ge 0\), इसलिए \(x^2-4 \ge -4\) है। न्यूनतम मान (x=0) पर (-4) है।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=x-2 -4) का परिसर क्या है?
What is the range of (f(x)=x-2 -4)?
#range
#quadratic-function
#class11
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
यदि \(A=\{-1,0,1\}\) और (f(x)=x-2 ), तो परिसर क्या है?
If \(A=\{-1,0,1\}\) and (f(x)=x-2 ), what is the range?
#finite-domain
#range
#square-function
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ({0,1})
B ({-1,0,1})
C ({1,2})
D ({-1,1})
Explanation opens after your attempt
Correct Answer
A. ({0,1})
Step 1
Concept
((-1)2 =1), \(0^2=0\), and \(1^2=1\). The distinct output values are ({0,1}).
Step 2
Why this answer is correct
The correct answer is A. ({0,1}). ((-1)2 =1), \(0^2=0\), and \(1^2=1\). The distinct output values are ({0,1}).
Step 3
Exam Tip
((-1)2 =1), \(0^2=0\), और \(1^2=1\) हैं। अलग-अलग प्राप्त मान ({0,1}) हैं।
Login to save your score, XP, coins and progress. Login
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
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
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
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=x-2 +4) का सबसे छोटा मान क्या है?
What is the least value of (f(x)=x-2 +4)?
#minimum
#quadratic-function
#range
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (4)
B (0)
C (-4)
D (2)
Explanation opens after your attempt
Step 1
Concept
The least value of \(x^2\) is (0). Therefore the least value of \(x^2+4\) is (4).
Step 2
Why this answer is correct
The correct answer is A. (4). The least value of \(x^2\) is (0). Therefore the least value of \(x^2+4\) is (4).
Step 3
Exam Tip
\(x^2\) का सबसे छोटा मान (0) होता है। इसलिए \(x^2+4\) का सबसे छोटा मान (4) है।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=x-2 +4) का परिसर क्या है?
What is the range of (f(x)=x-2 +4)?
#range
#quadratic-function
#class11
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
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
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
वास्तविक मान वाले फलन का अर्थ क्या है?
What does a real valued function mean?
#real-valued-functions
#definition
#class11
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
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
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
फलन \(f:A\to\mathbb{R}\) में \(\mathbb{R}\) सामान्यतः क्या दर्शाता है?
In the function \(f:A\to\mathbb{R}\), what does \(\mathbb{R}\) usually represent?
#codomain
#real-valued-functions
#notation
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A सहप्रांत / Codomain
B प्रांत / Domain
C केवल परिसर / Only range
D रिक्त समुच्चय / Empty set
Explanation opens after your attempt
Correct Answer
A. सहप्रांत / Codomain
Step 1
Concept
In \(f:A\to\mathbb{R}\), \(\mathbb{R}\) is the set where outputs are expected to lie. It is called the codomain.
Step 2
Why this answer is correct
The correct answer is A. सहप्रांत / Codomain. In \(f:A\to\mathbb{R}\), \(\mathbb{R}\) is the set where outputs are expected to lie. It is called the codomain.
Step 3
Exam Tip
\(f:A\to\mathbb{R}\) में \(\mathbb{R}\) वह समुच्चय है जिसमें मान जाने हैं। यह सहप्रांत कहलाता है।
Login to save your score, XP, coins and progress. Login
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
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
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
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=\sqrt{2x-6}) का प्रांत क्या है?
What is the domain of (f(x)=\sqrt{2x-6})?
#domain
#square-root
#linear-inequality
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \([3,\infty\))
B (\(3,\infty\))
C (\(-\infty,3]\)
D \(\mathbb{R}\)
Explanation opens after your attempt
Correct Answer
A. \([3,\infty\))
Step 1
Concept
For the square root, \(2x-6 \ge 0\) is required. This gives \(x \ge 3\).
Step 2
Why this answer is correct
The correct answer is A. \([3,\infty\)). For the square root, \(2x-6 \ge 0\) is required. This gives \(x \ge 3\).
Step 3
Exam Tip
वर्गमूल के लिए \(2x-6 \ge 0\) होना चाहिए। इससे \(x \ge 3\) मिलता है।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=\sqrt{4-2x}) का प्रांत क्या है?
What is the domain of (f(x)=\sqrt{4-2x})?
#domain
#square-root
#inequality
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (\(-\infty,2]\)
B \([2,\infty\))
C (\(-\infty,2\))
D \(\mathbb{R}-{2}\)
Explanation opens after your attempt
Correct Answer
A. (\(-\infty,2]\)
Step 1
Concept
The condition \(4-2x \ge 0\) gives \(x \le 2\). Thus the domain is (\(-\infty,2]\).
Step 2
Why this answer is correct
The correct answer is A. (\(-\infty,2]\). The condition \(4-2x \ge 0\) gives \(x \le 2\). Thus the domain is (\(-\infty,2]\).
Step 3
Exam Tip
शर्त \(4-2x \ge 0\) से \(x \le 2\) मिलता है। इसलिए प्रांत (\(-\infty,2]\) है।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=|x|+2) का परिसर क्या है?
What is the range of (f(x)=|x|+2)?
#modulus-function
#range
#class11
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=3-|x|) का अधिकतम मान क्या है?
What is the maximum value of (f(x)=3-|x|)?
#modulus-function
#maximum
#range
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (3)
B (0)
C (-3)
D (6)
Explanation opens after your attempt
Step 1
Concept
The minimum value of (|x|) is (0), so (3-|x|) is maximum at (3). This occurs at (x=0).
Step 2
Why this answer is correct
The correct answer is A. (3). The minimum value of (|x|) is (0), so (3-|x|) is maximum at (3). This occurs at (x=0).
Step 3
Exam Tip
(|x|) का न्यूनतम मान (0) है, इसलिए (3-|x|) अधिकतम (3) होगा। यह (x=0) पर मिलता है।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=3-|x|) का परिसर क्या है?
What is the range of (f(x)=3-|x|)?
#range
#modulus-function
#class11
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
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
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
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
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=(x-1)2 ) का परिसर क्या है?
What is the range of (f(x)=(x-1)2 )?
#range
#quadratic-function
#class11
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=(x+2)2 +1) का परिसर क्या है?
What is the range of (f(x)=(x+2)2 +1)?
#range
#quadratic-function
#minimum
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \([1,\infty\))
B \([0,\infty\))
C \([-2,\infty\))
D \(\mathbb{R}\)
Explanation opens after your attempt
Correct Answer
A. \([1,\infty\))
Step 1
Concept
The minimum value of ((x+2)2 ) is (0). Therefore the whole function has minimum value (1).
Step 2
Why this answer is correct
The correct answer is A. \([1,\infty\)). The minimum value of ((x+2)2 ) is (0). Therefore the whole function has minimum value (1).
Step 3
Exam Tip
((x+2)2 ) का न्यूनतम मान (0) है। इसलिए पूरा फलन न्यूनतम (1) देता है।
Login to save your score, XP, coins and progress. Login
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
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
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
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
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
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=\frac{1}{\sqrt{x-1}}) का प्रांत क्या है?
What is the domain of (f(x)=\frac{1}{\sqrt{x-1}})?
#domain
#square-root
#rational-function
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (\(1,\infty\))
B \([1,\infty\))
C (\(-\infty,1]\)
D \(\mathbb{R}\)
Explanation opens after your attempt
Correct Answer
A. (\(1,\infty\))
Step 1
Concept
The denominator is \(\sqrt{x-1}\), so (x-1>0) is required. Thus (x>1), and the domain is (\(1,\infty\)).
Step 2
Why this answer is correct
The correct answer is A. (\(1,\infty\)). The denominator is \(\sqrt{x-1}\), so (x-1>0) is required. Thus (x>1), and the domain is (\(1,\infty\)).
Step 3
Exam Tip
हर में \(\sqrt{x-1}\) है, इसलिए (x-1>0) चाहिए। इस कारण (x>1) और प्रांत (\(1,\infty\)) है।
Login to save your score, XP, coins and progress. Login
यदि (f(x)=|x+1|-3), तो इसका न्यूनतम मान क्या है?
If (f(x)=|x+1|-3), what is its minimum value?
#modulus-function
#minimum
#range
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (-3)
B (0)
C (1)
D (-1)
Explanation opens after your attempt
Step 1
Concept
The minimum value of (|x+1|) is (0). Therefore the minimum value of (|x+1|-3) is (-3).
Step 2
Why this answer is correct
The correct answer is A. (-3). The minimum value of (|x+1|) is (0). Therefore the minimum value of (|x+1|-3) is (-3).
Step 3
Exam Tip
(|x+1|) का न्यूनतम मान (0) है। इसलिए (|x+1|-3) का न्यूनतम मान (-3) है।
Login to save your score, XP, coins and progress. Login
