JEE Main 2022 · 25 Jun · Shift 1 · Mathematics Q6

← JEE Main 2022 · 25 Jun · Shift 1

MathematicsSingle correct+4 / -1Question 6 of 90

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 ______.

\dfrac1{49}

\dfrac3{49}

\dfrac{43}{49}

\dfrac{91}{49}

Answer and worked solution

Official answer: A

Inverse function. $g=f^{-1}$ , so $g'(63)=\dfrac1{f'(g(63))}$ .

Find $g(63)$ . $t^3+t-5=63$ gives $t=4$ .

Value. $f'(4)=3(16)+1=49$ , so $g'(63)=\dfrac1{49}$ .

(A)

Topics:Derivatives of standard functions Composition and inverse functions

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JEE Main 2022 · 25 Jun · Shift 1, Mathematics question 6