Let g: $$R \rightarrow R$$ be a differentiable function with g(0) = 0, g'(0) = 0 and $$g’(1) \neq 0$$. Let
$$f(x) = \begin{cases}\frac{x}{|x|}g(x) & x \neq 0\\0 & x = 0\end{cases}$$
and $$h(x) = e^{|x|}$$ for all $$x \in R$$. Let (f o h) (x) denote f(h(x)) and (h o 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 o h is differentiable at x = 0

D

h o f is differentiable at x = 0