JEE Mains · Maths · STD 11- 2. Relation and Function
The domain of \(f(x)=\frac{\log _{(x+1)}(x-2)}{e^{\log _e x}-(2 x+3)}, x \in R\) is
- A \(R -\{1-3\}\)
- B \((2, \infty)-\{3\}\)
- C \((-1, \infty)-\{3\}\)
- D \(R -\{3\}\)
Answer & Solution
Correct Answer
(B) \((2, \infty)-\{3\}\)
Step-by-step Solution
Detailed explanation
\(x-2>0 \Rightarrow x>2\) \(x+1 > 0 \Rightarrow x > -1\) \(x+1 \neq 1 \Rightarrow x \neq 0 \text { and } x > 0\) Denominator \(x^2-2 x-3 \neq 0\) \((x-3)(x+1) \neq 0\) \(x \neq-1,3\) So Ans \((2, \infty)-\{3\}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let \(f(\mathrm{x})=\left|2 \mathrm{x}^2+5\right| \mathrm{x}|-3|, \mathrm{x} \in \mathrm{R}\). If \(\mathrm{m}\) and \(\mathrm{n}\) denote the number of points where \(f\) is not continuous and not differentiable respectively, then \(m+n\) is equal to :JEE Mains 2024 Medium
- If an unbiased dice is rolled thrice, then the probability of getting a greater number in the \(i^{\text {th }}\) roll than the number obtained in the \((i-1)^{\text {th }}\) roll, \(i=2,3\), is equal to :JEE Mains 2024 Medium
- \(\mathop \smallint \limits_{ - \pi /2}^{\pi /2} \frac{{{{\sin }^2}x}}{{1 + {2^x}}}dx =\) . .. .JEE Mains 2018 Medium
- Let the line \(\mathrm{L}\) intersect the lines \(\mathrm{x}-2=-\mathrm{y}=\mathrm{z}-1,2(\mathrm{x}+1)=2(\mathrm{y}-1)=\mathrm{z}+1\) and be parallel to the line \(\frac{x-2}{3}=\frac{y-1}{1}=\frac{z-2}{2}\). Then which of the following points lies on \(\mathrm{L}\) ?JEE Mains 2024 Hard
- If two lines \(L_1\) and \(L_2\) in space, are defined by \({L_1} = \{ x = \sqrt \lambda y + \left( {\sqrt \lambda - 1} \right),z = \left( {\sqrt \lambda - 1} \right)y + \sqrt \lambda \} \) and \({L_2} = \{ x = \sqrt \mu y + \left( {1 - \sqrt \mu } \right),z = \left( {1 - \sqrt \mu } \right)y + \sqrt \mu \} \) then \(L_1\) is perpendicular to \(L_2\), for all non-negative reals \(\lambda \) and \( \mu \), such thatJEE Mains 2013 Hard
- Let the product of the focal distances of the point \(\mathrm{P}(4,2 \sqrt{3})\) on the hyperbola \(\mathrm{H}: \frac{\mathrm{x}^2}{\mathrm{a}^2}-\frac{\mathrm{y}^2}{\mathrm{~b}^2}=1\) be 32 .
Let the length of the conjugate axis of \(H\) be \(p\) and the length of its latus rectum be q . Then \(\mathrm{p}^2+\mathrm{q}^2\) is equal to _______JEE Mains 2025 Hard
More PYQs from JEE Mains
- Let \(\alpha\) and \(\beta\) be the roots of the equation \(\mathrm{x}^{2}-\mathrm{x}-1=0 .\) If \(\mathrm{p}_{\mathrm{k}}=(\alpha)^{\mathrm{k}}+(\beta)^{\mathrm{k}}, \mathrm{k} \geq 1,\) then which one of the following statements is not true?JEE Mains 2020 Hard
- If the tangent to the parabola \(y^2 = x\) at a point \(\left( {\alpha ,\beta } \right)\,,\,\left( {\beta > 0} \right)\) is also a tangent to the ellipse, \(x^2 + 2y^2 = 1\), then \(a\) is equal toJEE Mains 2019 Hard
- Let \(X\) be a random variable such that the probability function of a distribution is given by \(P(X=\) 0) \(=\frac{1}{2}, \mathrm{P}(\mathrm{X}=\mathrm{j})=\frac{1}{3^{j}}(\mathrm{j}=1,2,3, \ldots, \infty)\). Then the mean of the distribution and \(\mathrm{P}(\mathrm{X}\) is positive and even) respectively are:JEE Mains 2021 Medium
- Let a straight line \(L\) pass through the point \(P(2,-1,3)\) and be perpendicular to the lines \(\frac{x-1}{2}=\frac{y+1}{1}=\frac{z-3}{-2}\) and \(\frac{x-3}{1}=\frac{y-2}{3}=\frac{z+2}{4}\). If the line \(L\) intersects the \(y z\)-plane at the point \(Q\), then the distance between the points \(P\) and \(Q\) is :JEE Mains 2025 Medium
- Consider the sets \(\mathrm{A}=\left\{(\mathrm{x}, \mathrm{y}) \in \mathbb{R} \times \mathbb{R}: \mathrm{x}^2+\mathrm{y}^2=25\right\}\), \(\mathrm{B}=\left\{(\mathrm{x}, \mathrm{y}) \in \mathbb{R} \times \mathbb{R}: \mathrm{x}^2+9 \mathrm{y}^2=144\right\}, \mathrm{C}=\{(\mathrm{x}, \mathrm{y})\) \(\left.\in \mathbb{Z} \times \mathbb{Z}: x^2+y^2 \leq 4\right\}\), and \(D=A \cap B\). The total number of one-one functions from the set D to the set C is:JEE Mains 2025 Hard
- Let the area enclosed between the curves \(|y|=1-x^2\) and \(x^2+y^2=1\) be \(\alpha\). If \(9 \alpha=\beta \pi+\gamma ; \beta, \gamma\) are integers, then the value of \(|\beta-\gamma|\) equals.JEE Mains 2025 Medium