Let $g : \mathbb { R } \rightarrow \mathbb { R }$ be a differentiable function with $g ( 0 ) = 0 , g ^ { \prime } ( 0 ) = 0$ and $g ^ { \prime } ( 1 ) \neq 0$. Let $$f ( x ) = \left\{ \begin{array} { c c } \frac { x } { | x | } g ( x ) , & x \neq 0 \\ 0 , & x = 0 \end{array} \right.$$ and $h ( x ) = e ^ { | x | }$ for all $x \in \mathbb { R }$. Let $( f \circ h ) ( x )$ denote $f ( h ( x ) )$ and $( h \circ f ) ( x )$ denote $h ( f ( x ) )$. Then which of the following is (are) true? (A) $f$ is differentiable at $x = 0$ (B) $\quad h$ is differentiable at $x = 0$ (C) $f \circ h$ is differentiable at $x = 0$ (D) $h \circ f$ is differentiable at $x = 0$
Let $g : \mathbb { R } \rightarrow \mathbb { R }$ be a differentiable function with $g ( 0 ) = 0 , g ^ { \prime } ( 0 ) = 0$ and $g ^ { \prime } ( 1 ) \neq 0$. Let
$$f ( x ) = \left\{ \begin{array} { c c } \frac { x } { | x | } g ( x ) , & x \neq 0 \\ 0 , & x = 0 \end{array} \right.$$
and $h ( x ) = e ^ { | x | }$ for all $x \in \mathbb { R }$. Let $( f \circ h ) ( x )$ denote $f ( h ( x ) )$ and $( h \circ f ) ( x )$ denote $h ( f ( x ) )$. Then which of the following is (are) true?\\
(A) $f$ is differentiable at $x = 0$\\
(B) $\quad h$ is differentiable at $x = 0$\\
(C) $f \circ h$ is differentiable at $x = 0$\\
(D) $h \circ f$ is differentiable at $x = 0$