STD 12 - 7.1 inderfinite integral — Mathematics STD 12 Science — Question

Let $f(x)=\left\{\begin{array}{cc}\frac{x}{|x|} g(x), & x \neq 0 \\ 0, & x=0\end{array}\right.$

and $h(x)=e^{\text {ld }}$ for all $x \in R$. 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 $x=0$

$(B)$ $h$ is differentiable at $x=0$

$(C)$ $f \circ h$ is differentiable at $x=0$

$(D)$ $h \circ f$ is differentiable at $x=0$