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Let g: RR to RR be a differentiable func...

Let `g: RR to RR` be a differentiable function with `g(0)=0,g'(0)=0` and `g'(1)ne0`.
Let `f(x)={{:((x)/(|x|)g(x)", "xne0),(0", "x =0):}" and "h(x)=e^(|x|)" for all "x inRR.`
Let `("foh")(x)` denote `f(h(x))` and `("hof")(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

foh is differentiable at x = 0

D

hof is differentiable at x = 0

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