Question

Given the functions `g(x) = 3/(x - 1)`, `f(x) = (x - 1)/(x - 3)` what is g(f(x))?

Answer 1

`(3x-9)/2`

Explanation:

To find `g(f(x))`, take `f(x)`, or `color(blue)((x-1)/(x-3))`, and plug it in for `x` in `g(x)`, or `3/(color(blue)(x)-3)`.

You get that

`g(f(x))=3/(color(blue)((x-1)/(x-3))-1)`

Multiply everything by `x-3`.

`=3/((x-1)/(x-3)-1)((x-3)/(x-3))=(3(x-3))/((x-1)-1(x-3))`

`=(3(x-3))/(x-1-x+3)=(3x-9)/2`