jee-advanced 2002 Q21

jee-advanced · India · screening Differentiation from First Principles
21. The domain of the derivative of the function
$$f ( x ) = \left\{ \begin{array} { c } \tan ^ { - 1 } x , \text { if } | x | \leq 1 \\ \frac { 1 } { 2 } ( | x | - 1 ) , \text { if } | x | > 1 \end{array} \right\} \text { is }$$
(A) $\mathrm { R } - \{ 0 \}$
(B) $\mathrm { R } - \{ 1 \}$
(C) $\mathrm { R } - \{ - 1 \}$
(D) $\mathrm { R } - \{ - 1,1 \}$
21. The domain of the derivative of the function

$$f ( x ) = \left\{ \begin{array} { c } 
\tan ^ { - 1 } x , \text { if } | x | \leq 1 \\
\frac { 1 } { 2 } ( | x | - 1 ) , \text { if } | x | > 1
\end{array} \right\} \text { is }$$

(A) $\mathrm { R } - \{ 0 \}$\\
(B) $\mathrm { R } - \{ 1 \}$\\
(C) $\mathrm { R } - \{ - 1 \}$\\
(D) $\mathrm { R } - \{ - 1,1 \}$\\