Question

If `h(x)=(f-g)(x), f(x)=5x+2` how do you determine g(x) given `h(x)=sqrt(x-4)+5x+2`?

Answer 1

`g(x) = -sqrt(x-4)`

Explanation:

Firstly, it's important to note that `(f-g)(x)` is the same thing as `f(x) - g(x)`.

`h(x) = f(x) - g(x)`

We can substitute the function names out for the actual functions to find our answer.

`sqrt(x-4) + 5x + 2 = 5x + 2 - g(x)`
`sqrt(x-4) + cancel(5x + 2) = cancel(5x + 2) - g(x)`
`sqrt(x-4) = -g(x)`

`g(x) = -sqrt(x-4)`