Question

How do you find the inverse of `f(x) = 2x-4` and is it a function?

Answer 1

`f^-1 (x) = (x + 4)/2`

It is a functions, because every `x` value you use will have a unique y value. There is never a choice for what `y` will be.

Explanation:

The steps for finding the inverse of a function are:

1. Change f(x) to y
2. Swop x's and y's
3. make y the subject. ie y = ...
4. Change y to `f^-1(x)`

`f(x) = 2x - 4 " " rArr y = 2x -4`

`x " "= 2y - 4`
`x + 4 = 2y`

`y = (x + 4)/2 " this is what we want!"`

`f^-1 (x) = (x + 4)/2`