If f x = x 3 + 3 x + 1 and g x is the inverse function of f x , then the value of g ' 5 is equal to

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Question: Answered & Verified by Expert

If

f (x) = x^{3} + 3 x + 1

and

g (x)

is the inverse function of

f (x)

, then the value of

g^{'} (5)

is equal to

MathematicsDifferentiationJEE Main

Options:

A $3$
B $\frac{1}{3}$
C $\frac{1}{6}$
D $6$

Solution:

2667 Upvotes Verified Answer

The correct answer is:

\frac{1}{6}

∵

f (x), g (x)

are inverse function of each other

∴

g^{'} (f (x)) = \frac{1}{f^{'} (x)}

Now put

x = 1; g^{'} (f (1)) = \frac{1}{f^{'} (1)}

Hence,

g^{'} (5) = \frac{1}{{(3 x^{2} + 3)}_{x = 1}} = \frac{1}{6}

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