Question

Let $ƒ : R→R$ be defined as $ƒ(x) = x^3 + x – 5$ . If g(x) is a function such that $ƒ(g(x)) = x$, ∀‘x‘∈R. Then $g^′(63)$ is equal to_____.

• A. $\frac {1}{49}$
• B. $\frac {3}{49}$
• C. $\frac {43}{49}$
• D. $\frac {91}{49}$

Answer 1

Answer: (A)

$\frac {1}{49}$

Answer 2

$ƒ(x) = 3x^2 \+ 1$
$ƒ^′(x)$ is bijective function
and $ƒ(g(x)) = x⇒g(x$) is inverse of $ƒ(x)$
$g(ƒ(x)) = x$
$g^′(f(x)).f^′(x) = 1$
$g^′(f(x)) = \frac {1}{3x^2+1}$
Put $x = 4$ we get
$g^′(63)=\frac {1}{49}$

So, the correct option is (A): $\frac {1}{49}$