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  • The domain of the derivative of the function <img alt="\mathrm{f(x)=\left\{\begin{array}{c} \tan ^{-1} x ; \text { if }|x| \leq 1 \\ \frac{1}{2}(|x|-1) ; \text { if }|x|>1 \text { is } \e

The domain of the derivative of the function
\mathrm{f(x)=\left\{\begin{array}{c} \tan ^{-1} x ; \text { if }|x| \leq 1 \\ \frac{1}{2}(|x|-1) ; \text { if }|x|>1 \text { is } \end{array}\right.}

 

Option: 1

\mathrm{R-\{0\}}


Option: 2

\mathrm{R-\{1\}}


Option: 3

\mathrm{R-\{-1\}}


Option: 4

\mathrm{R-\{-1,1\}}


Answers (1)

best_answer

\mathrm{f(x)=\left\{\begin{array}{l} \tan ^{-1} x ;-1 \leq x \leq 1 \\ \frac{1}{2}(x-1) ; x>1 \\ \frac{1}{2}(-x-1) ; x<-1 \end{array}\right.}

Given function, f(x)  is discontinuous at  x=1\mathrm{x=1}  and \mathrm{x=-1} 

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