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Question

If g is the inverse of a function f and f'(x)=11+x5, then g'(x) is equal to:

A
1+x5
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B
5x4
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C
11+{g(x)}5
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D
1+{g(x)}5
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Solution

The correct option is D 1+{g(x)}5
g(x)=f1x
f(g(x))=x
f(g(x))g(x)=1
g(x)=1f(g(x))...(1)
As given, f(x)=11+x5
f(g(x))=11+{g(x)}5
from equation (1)
g(x)=1+{g(x)}5

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