Mathematics

Problem

Let

f: \mathbb{R} \to \mathbb{R}

be defined as

f(x) = x^3 + x - 5

. If

g(x)

is a function such that

f(g(x)) = x

\forall x \in \mathbb{R}

, then

g'(63)

is equal to _____ . [JEE MAINS - ONLINE - 2022] (1)

\frac{1}{49}

(2)

\frac{3}{49}

(3)

\frac{43}{49}

(4)

\frac{91}{49}