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Question
If the function f : R → R be defined by f(x) = 2x − 3 and g : R → R by g(x) = x3 + 5, then find the value of (fog)−1 (x).
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Solution
Given:
f(x) = 2x − 3
g(x) = x3 + 5
(fog)(x)=f[g(x)]
=f(x3+5)
=2(x3+5)−3
=2x3+10−3
=2x3+7
Let (fog)(x)=y
⇒2x3+7=y
`=>x=((y-7)/2)^(1/3)`
`=>(fog)^-1 (y)=((y-7)/2)^(1/3)`
Thus, (fog)−1: R→R be defined by `(fog)^-1 (x)=((x-7)/2)^(1/3)`
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