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Let g: R -> R be a differentiable functi...

Let `g: R -> R` be a differentiable function with `g(0) = 0,g'(1)=0,g'(1)!=0`.Let `f(x)={x/|x|g(x), 0 !=0 and 0,x=0` and `h(x)=e^(|x|)` for all `x in R`. Let `(foh)(x)` denote `f(h(x)) and (hof)(x)` denote `h(f(x))`. Then which of thx!=0 and e 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

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The correct Answer is:
A, D
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