The domain of the derivative of the function f(x)= cases ^ -1 x,&|x| 1…

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

The domain of the derivative of the function

f(x)=\begin{cases}\tan^{-1}x,&|x|\leq1\\\frac12(|x|-1),&|x|>1\end{cases}

is (a)

\mathbb{R}\setminus\{0\}

(b)

\mathbb{R}\setminus\{1\}

(c)

\mathbb{R}\setminus\{-1\}

(d)

\mathbb{R}\setminus\{-1,1\}