JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
The domain of the function \(f(x)=\sin ^{-1}\left(\frac{3 x^{2}+x-1}{(x-1)^{2}}\right)+\cos ^{-1}\left(\frac{x-1}{x+1}\right)\) is :
- A \(\left[0, \frac{1}{4}\right]\)
- B \([-2,0] \cup\left[\frac{1}{4}, \frac{1}{2}\right]\)
- C \(\left[\frac{1}{4}, \frac{1}{2}\right] \cup\{0\}\)
- D \(\left[0, \frac{1}{2}\right]\)
Answer & Solution
Correct Answer
(C) \(\left[\frac{1}{4}, \frac{1}{2}\right] \cup\{0\}\)
Step-by-step Solution
Detailed explanation
\(f(x)=\sin ^{-1}\left(\frac{3 x^{2}+x-1}{(x-1)^{2}}\right)+\cos ^{-1}\left(\frac{x-1}{x+1}\right)\) \(-1 \leq \frac{x-1}{x+1} \leq 1 \Rightarrow 0 \leq x<\infty...(1)\)…
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
- If \(\alpha \neq \mathrm{a}, \beta \neq \mathrm{b}, \gamma \neq \mathrm{c}\) and \(\left|\begin{array}{lll}\alpha & \mathrm{b} & \mathrm{c} \\ \mathrm{a} & \beta & \mathrm{c} \\ \mathrm{a} & \mathrm{b} & \gamma\end{array}\right|=0\),then \(\frac{a}{\alpha-a}+\frac{b}{\beta-b}+\frac{\gamma}{\gamma-c}\) is equal to :JEE Mains 2024 Hard
- Let \(\vec{a_k} = (\tan\theta_k)\hat{i} + \hat{j}\) and \(\vec{b_k} = \hat{i} - (\cot\theta_k)\hat{j}\), where \(\theta_k = \dfrac{2^{k-1}\pi}{2^n + 1}\), for some \(n \in \mathbb{N}\), \(n > 5\). Then the value of \(\dfrac{\displaystyle\sum_{k=1}^{n}|\vec{a_k}|^2}{\displaystyle\sum_{k=1}^{n}|\vec{b_k}|^2}\) is _____.JEE Mains 2026 Hard
- If the solution curve of the differential equation \(\frac{d y}{d x}=\frac{x+y-2}{x-y}\) passes through the point \((2,1)\) and \(( k +1,2), k >0\), then.JEE Mains 2022 Hard
- Consider the system of linear equations \(-x+y+2 z=0\) \(3 x-a y+5 z=1\) \(2 x-2 y-a z=7\) Let \(S_{1}\) be the set of all \(\mathrm{a} \in {R}\) for which the system is inconsistent and \(S_{2}\) be the set of all \(a \in {R}\) for which the system has infinitely many solutions. If \(n\left(S_{1}\right)\) and \(n\left(S_{2}\right)\) denote the number of elements in \(S_{1}\) and \(\mathrm{S}_{2}\) respectively, thenJEE Mains 2021 Hard
- For the function \(f(x)=\sin x+3 x-\frac{2}{\pi}\left(x^2+x\right) \text {, where } x \in\left[0, \frac{\pi}{2}\right] \text {, }\) consider the following two statements : (\(I\)) \(\mathrm{f}\) is increasing in \(\left(0, \frac{\pi}{2}\right)\). (\(II\)) \(\mathrm{f}^{\prime}\) is decreasing in \(\left(0, \frac{\pi}{2}\right)\). Between the above two statements,JEE Mains 2024 Hard
- Equation of a common tangent to the circle, \(x^2 + y^2 - 6x = 0\) and the parabola, \(y^2 = 4x\) , isJEE Mains 2019 Hard
More PYQs from JEE Mains
- The total number of matrices \(A = \left[ {\begin{array}{*{20}{c}}
0&{2x}&{2x}\\
{2y}&y&{ - y}\\
1&{ - 1}&1
\end{array}} \right];\,\left( {x,y \in R,\,x \ne y} \right)\) for which \({A^T}A = 3{I_3}\)JEE Mains 2019 Hard - If for \(p \neq q \neq 0\), then function,\(f(x)=\frac{\sqrt[7]{p(729+x)}-3}{\sqrt[3]{729+q x}-9}\)is continuous at \(x=0\), thenJEE Mains 2022 Hard
- If \(\alpha, \beta\) are the roots of the equation, \(x^2-x-1=0\) and \(S_n=2023 \alpha^n+2024 \beta^n\), thenJEE Mains 2024 Hard
- For \(0<\theta<\pi / 2\), if the eccentricity of the hyperbola \(\mathrm{x}^2-\mathrm{y}^2 \operatorname{cosec}^2 \theta=5\) is \(\sqrt{7}\) times eccentricity of the ellipse \(x^2 \operatorname{cosec}^2 \theta+y^2=5\), then the value of \(\theta\) is :JEE Mains 2024 Medium
- The function \(\mathrm{f}: \mathrm{N}-\{1\} \rightarrow \mathrm{N}\); defined by \(\mathrm{f}(\mathrm{n})=\) the highest prime factor of \(n\), is :JEE Mains 2024 Medium
- Let \(f: \mathrm{R} \rightarrow \mathrm{R}\) be a function given by \(f(x)= \begin{cases}\frac{1-\cos 2 x}{x^2} & , x<0 \\ \alpha & , x=0, \text { where } \alpha, \beta \in R \text {. If } \\ \frac{\beta \sqrt{1-\cos x}}{x} & , x>0\end{cases}\) \(f\) is continuous at \(\mathrm{x}=0\), then \(\alpha^2+\beta^2\) is equal to :JEE Mains 2024 Medium