If `f:IRtoIRtoIR` be two functions given by `f(x)=2x-3andg(x)=x^(3)+5" than "(fog)^(-1)(x)` is equal to

Options

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

Explanation

`f(x)=2x-3`
`g(x)=x^(3)+5`
`fog(x)=f[g(x)]=f(x^(3)+5)`
`=2(x^(3)+5)-3`
`fog(x)=2x^(3)+7=y(say)`
`implies2x^(3)=y-7`
`impliesx=[(y-7)/(2)]^((1)/(3))`
`impliesfog^(-1)(y)=[(y-7)/(2)]^((1)/(3))`
`impliesfog^(-1)(x)=[(x-7)/(2)]^((1)/(3))`