Question

If `g(x)` is the inverse of `f(x)` and `f(x)=4x+ 12`, what is `g(x)`?

Answer 1

`g(x)=x/4-3`

Explanation:

set `y=4x+12`

subtract 12 from both sides

`y-12=4x`

Divide both sides by 4

`x=y/4-12/4`

`x=y/4-3`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Where there is a `x` write `y`
Where there is a `y` write `x`

Giving

`y=x/4-3`

`g(x)=x/4-3`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The inverse function is the original equation reflected about `y=x`