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Question

Let g(x) be the inverse of the function f(x) and f(x)=11+x3 Then g(x) is

A
11+(g(x))3
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B
11+(f(x))3
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C
1+(g(x))3
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D
1+(f(x))3
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Solution

The correct option is C 1+(g(x))3
Given that g(x) is inverse of f(x).

g(f(x))=xg(f(x)).f(x)=1

g(f(x))=1f(x)=1+x3

f(x)=y

g(y)=1f(x)=1+x3

x=f1(y)=g(y)..............................................................(i)

g(y)=1+g3(y) by (i)

g(x)=1+g3(x)

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