Question

Let `f(x) = 2 -x` and `f(g(x)) = (2x-3)/x`, how do you find g(x)?

Answer 1

I found `g(x)=-3/x`

Explanation:

Consider that when you use `g(x)` you get:
`f(g(x))=2-g(x)=(2x-3)/x`
so:
`2-g(x)=(2x-3)/x`
`g(x)=2-(2x-3)/x`
`g(x)=(cancel(2x)cancel(-2x)-3)/x=-3/x`