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Question

If f(x)=(ax2+b)3 then a function g(x) such that f(g(x)) = g (f(x)) is given by

A
g(x)=(bx1/3a)1/2
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B
g(x)=1(ax2+b)3
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C
g(x)=(ax2+b)1/3
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D
g(x)=(x1/3ba)1/2
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Solution

The correct option is A g(x)=(bx1/3a)1/2
Let g(x) be f1x as f(f1(x))=x and f1(f(x))=x

3y=ax2+bx2= 3yba

x=(3yba)12

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