Let 
be a differential function with g(0) = 0, g ’ (0) = 0 and 
. Let 
and h(x) = e |x| for all 
. 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?
Text Solution
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(a,d)Differentiability of f(x) at x = 0
LHD 
RHD 
f(x) is differentiable at x = 0.
Differentiability of h(x) at x = 0
h'(0 + ) = 1, h(x) is an even function
hence non diff. at x = 0
Differentiability of f(h(x)) at x = 0
LHD 
RHD 
Since g ’ (1) 
0 
f(h(x)) is non diff. at x = 0
Differentiability of h(f(x)) at x = 0
LHD. 
RHD 
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