jee-advanced 2016 Q47

jee-advanced · India · paper1 Composite & Inverse Functions Derivative of an Inverse Function

Let $f:\mathbb{R} \rightarrow \mathbb{R}, g:\mathbb{R} \rightarrow \mathbb{R}$ and $h:\mathbb{R} \rightarrow \mathbb{R}$ 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
(A) $g'(2) = \frac{1}{15}$
(B) $h'(1) = 666$
(C) $h(0) = 16$
(D) $h(g(3)) = 36$

Let $f:\mathbb{R} \rightarrow \mathbb{R}, g:\mathbb{R} \rightarrow \mathbb{R}$ and $h:\mathbb{R} \rightarrow \mathbb{R}$ 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\\
(A) $g'(2) = \frac{1}{15}$\\
(B) $h'(1) = 666$\\
(C) $h(0) = 16$\\
(D) $h(g(3)) = 36$

Paper Questions

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