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

The correct option is A 1+{g(x)}5
Given f(x)=11+x5
Since g is inverse of f
fog(x)=x for all x
ddx|fog(x)|=1 for all x
f(g(x)).g(x)=1
f[g(x)]=1g(x)
11+[g(x)]5=1g(x) ................................................f(x)=11+x5
g(x)=1+[g(x)]5

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