Question

How do you find the inverse function of `y=2-x`?

Answer 1

`f(y) = 2 - y` or `x = 2 -y` or `f^(-1)(x) = 2 - x`
(They're the same thing, it's just a notational difference)

Explanation:

To find the inverse of any function, first isolate `x`

`y = 2 -x`
`y - 2 = -x`
`2 - y = x`

Replace `x` for `f(y)`

`f(y) = x = 2 - y`

Commonly though, inverse functions are represented in the form of `f^(-1)(x)`, so replace `y` for `x`

`f^(-1)(x) = 2 - x`

I personally think it muddles the point, since the function isn't taking `x` as an argument but that's the convention, so it's important to keep it in mind.