Question

Given f(x)=3x+12, what is f(f^-1(3))

Answer 1

3

Explanation:

We know:

`f\bigg(f^(-1)(x)\bigg)=x`

Therefore

`f\bigg(f^(-1)(3)\bigg)=3`

Other method.

Find
`f^(-1)(x)`

`f(x)=3x+12\to y=3x+12`

exchange x to y and vice versa:

`x=3y+12`

solve for y:

`3y+12=x` subtract 12 from both sides

`3y=x-12` divide both sides by 3

`y=(x-12)/(3)\to f^(-1)(x)=(x-12)/(3)`

`f\bigg(f^(-1)(x)\bigg)` replace x in f(x) with the expression
`(x-12)/(3)`

`f\bigg(f^(-1)(x)\bigg)=3\cdot(x-12)/(3)+12=x-12+12=x`

`f\bigg(f^(-1)(3)\bigg)` - put x = 3 to
`f\bigg(f^(-1)(x)\bigg)`

`f\bigg(f^(-1)(3)\bigg)=3`