The domain of the function f(x)=sin^-1 (frac3x^2+x-1(x-1)^2 )+cos^-1 ((x-1)/(x+1) ) is :

Functions: The domain of the function f(x)=sin^-1 (frac3x^2+x-1(x-1)^2 )+cos^-1… | JEE Main 2021

JEE Main 2021 (Online) 31st August Evening ShiftQuestion 1

The domain of the function $f(x)=\sin^{-1}\left(\frac{3x^{2}+x-1}{(x-1)^{2}}\right)+\cos^{-1}\left(\frac{x-1}{x+1}\right)$ is :

Functions

$\left[0,\frac{1}{4}\right]$$\left[0,\frac{1}{2}\right]$$\left[\frac{1}{4},\frac{1}{2}\right]\cup\{0\}$✓ Correct answer$[-2,0]\cup\left[\frac{1}{4},\frac{1}{2}\right]$

Solution

$\left|\frac{x-1}{x+1}\right|\le1\Rightarrow x\ge0$; $\left|\frac{3x^2+x-1}{(x-1)^2}\right|\le1$ gives $2x^2+3x-2\le0$ and $4x^2-x\ge0$, i.e. $-2\le x\le\frac12$ and ($x\le0$ or $x\ge\frac14$). Domain $=\{0\}\cup\left[\frac14,\frac12\right]$.

Functions - JEE Mathematics question (JEE Main 2021 (Online) 31st August Evening Shift)

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