Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Let g: R → R be a differentiable function with g(0) = 0, g'(0) = 0 and g'
A
≠ 0. Let f(x) = 
and h(x) = e |x| for all x ∈ R. Let (foh)(x) denote f(h(x)) and (hof)(x) denote h(f(x)). Then which of the following is(are) true? f is differentiable at x = 0
and h(x) = e |x| for all x ∈ R. Let (foh)(x) denote f(h(x)) and (hof)(x) denote h(f(x)). Then which of the following is(are) true? 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
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(a,d)
Sol. g(0) = 0, g ′ (0) = 0 g ′ ≠ 0
h(x) = e |x|
= 
, 
= 
= g ′ (0) = 0
= 
= 
g ′ (0) = 0
= 1 & 
So h(x) is non derivable. at x = 0
Now 
= 
R(f ′ (h(x))) = 
= 
= g ′
= – g ′ Hence 
is non derivable at x = 0
Since x = 0 is repeated root of g(x) So 
is differetiable at x = 0
hence ,
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