The domain of the function f(x) = log \((x^2-4)\) is:
- [2,∞)
- (-∞,-2) U (2,∞)
- (2,∞)
- (-∞, -2] U (-2, −1)
The Correct Option is B
Solution and Explanation
To find the domain of the function \( f(x) = \log(x^2-4) \), we need to ensure the argument of the logarithm is positive.
The expression \( x^2-4 \) must be greater than zero:
\( x^2-4 > 0 \)
Solve the inequality:
\( x^2 > 4 \)
This implies:
\( x > 2 \) or \( x < -2 \)
The solution provides the domain as a union of two intervals:
\((-∞, -2) \cup (2, ∞)\)
Top Questions on Relations and Functions
- The number of relations, defined on the set \{a, b, c, d\}, which are both reflexive and symmetric, is equal to:
- JEE Main - 2026
- Mathematics
- Relations and Functions
- Consider two sets \[ A = \{ x \in \mathbb{Z} : |(|x-3|-3)| \le 1 \} \] and \[ B = \left\{ x \in \mathbb{R} - \{1,2\} : \frac{(x-2)(x-4)}{x-1}\,\log_e(|x-2|) = 0 \right\}. \] Then the number of onto functions \( f : A \to B \) is equal to
- JEE Main - 2026
- Mathematics
- Relations and Functions
Let \( A = \{0,1,2,\ldots,9\} \). Let \( R \) be a relation on \( A \) defined by \((x,y) \in R\) if and only if \( |x - y| \) is a multiple of \(3\). Given below are two statements:
Statement I: \( n(R) = 36 \).
Statement II: \( R \) is an equivalence relation.
In the light of the above statements, choose the correct answer from the options given below.- JEE Main - 2026
- Mathematics
- Relations and Functions
- Let \( A = \{1,2,3,\ldots,9\} \) and \( R \subset A \times A \) be defined by \[ (x,y) \in R \iff |x-y| \text{ is a multiple of } 3. \] Consider the following statements:
S\(_1\): Number of elements in \( R \) is 36.
S\(_2\): \( R \) is an equivalence relation.
Which of the following is correct?- JEE Main - 2026
- Mathematics
- Relations and Functions
- Let the sets \[ A = \{x : |x - 3| - 3 \le 1,\; x \in \mathbb{Z}\} \] \[ B = \left\{ x : x \in \mathbb{R},\; x \ne 1,2,\; \frac{(x-2)(x-4)}{(x-1)} \log_e |x-2| = 0 \right\} \] Then the number of onto functions from \( A \) to \( B \) is:
- JEE Main - 2026
- Mathematics
- Relations and Functions
Questions Asked in CUET exam
- Find the ratio of de-Broglie wavelengths of deuteron having energy E and \(\alpha\)-particle having energy 2E :
- CUET (UG) - 2026
- Dual nature of radiation and matter
- The angles of elevation of the top of a tower from two points at a distance of 5 meters and 20 meters along the same straight line from the base of the tower, are complementary. Find the height of the tower.
- CUET (UG) - 2025
- Trigonometry
- Had he ________ the importance of the meeting, he would have made sure to attend.
Rearrange the following parts to form a meaningful and grammatically correct sentence:
P. a healthy diet and regular exercise
Q. are important habits
R. that help maintain good physical and mental health
S. especially in today's busy world- CUET (UG) - 2025
- Sentence Arrangement
- The following solutions were prepared by dissolving 1 g of solute in 1 L of the solution. Arrange the following solutions in decreasing order of their molarity: (A) Glucose (molar mass = 180 g mol$^{-1}$)
(B) NaOH (molar mass = 40 g mol$^{-1}$)
(C) NaCl (molar mass = 58.5 g mol$^{-1}$)
(D) KCl (molar mass = 7(4)5 g mol$^{-1}$)
- CUET (UG) - 2025
- Mole concept and Molar Masses