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Question

Let f(x) and g(x) be two bijective functions, where f(x)=3x+5 and g(x)=ex32 , then (fog(x))1 is equal to

A
lnx
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B
ln(1x)
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C
ln(1+x)
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D
ex+1
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Solution

The correct option is C ln(1+x)
Given: f(x)=3x+5 and g(x)=ex32
fog(x)=ex6+5fog(x)=ex1
Let y=(fog(x))=ex1
1+y=exx=ln(1+y)
Replace x with y, we get
(fog(x))1=ln(1+x)

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