Let g:\mathbb{R}\to\mathbb{R} be a differential function with g(0)=0,g'(0)=0\text{and}g'(1)\neq0 Let f(x)=\\begin{array}{c}x/|x|\end{array}g(x)\text{,},x\neq0;0\text{,},x=0 and h(x)=e^{|x|}\text{for all}x∊\mathbb{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? [JEE Adv 2015 P1]

f\text{is differentiable at}x=0

h\text{is differentiable at}x=0

JEE Advanced 2015 Paper 1

Section: Mathematics

Question : 57 of 60

Marks: +1, -0

Let g:ℝ→ℝ be a differential function with g(0)=0,g′(0)=0‌and‌g′(1)≠0
Let f(x)={

|x|

g(x),

x≠0

x=0

and h(x)=e|x|‌for all‌x∊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?

[JEE Adv 2015 P1]

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