Let `f:R to R, g: R to R` be two functions given by `f(x)=2x-3,g(x)=x^(3)+5`. Then `(fog)^(-1)` is equal to

Options

A. `((x+7)/(2))^(1//3)`
B. `(x-(7)/(2))^(1//3)`
C. `((x-2)/(7))^(1//3)`
D. `((x-7)/(2))^(1//3)`

Answer

D

Explanation

`f : R rarr R`
g : R `rarr` R
f(x) = 2x - 3
`g(x) = x^(3) + 5`
implies `(fog)(x)=f(g(x))=f(x^(3)+5)=2(x^(3)+5)-3`
`=2x^(3)+7`
Now, let `y = 2x^(3) + 7`
`2x^(3) = y - 7`
`x=((y-7)/(2))^(1//3)`
Replacing x by y, we get
`y=((x-7)/(2))^(1//3)`
`therefore (fog)^(-1)(x)=((x-7)/(2))^(1//3)`