JEE Advanced 2016 Paper 1 Mathematics Q11

Mathematics

Problem

Let

f:\mathbb R\to\mathbb R

g:\mathbb R\to\mathbb R

and

h:\mathbb R\to\mathbb R

be differentiable functions such that

f(x)=x^3+3x+2

g(f(x))=x

and

h(g(g(x)))=x

for all

x\in\mathbb R

. Then