If g ( x ) is the inverse function of f ( x ) and f ′ ( x ) = 1 1 + x 4 , then g ′ ( x ) is

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Question: Answered & Verified by Expert

If

g (x)

is the inverse function of

f (x)

and

f^{'} (x) = \frac{1}{1 + x^{4}},

then

g^{'} (x)

is

MathematicsDifferentiationMHT CETMHT CET 2017

Options:

A $1 + {[g (x)]}^{4}$
B $1 - {[g (x)]}^{4}$
C $1 + {[f (x)]}^{4}$
D $\frac{1}{1 + {[g (x)]}^{4}}$

Solution:

2494 Upvotes Verified Answer

The correct answer is:

1 + {[g (x)]}^{4}

g = f^{- 1}

f (g (x)) = x

Differentiate w.r.t x

f^{'} (g (x)) . g^{'} (x) = 1

∴ \frac{1}{1 + {(g (x))}^{4}} . g^{'} (x) = 1

g^{'} (x) = 1 + {[g (x)]}^{4}

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