Question

How do you find `(fog)(x)` given `f(x)=x^2+7` and `g(x)=x-3`?

Answer 1

`(fog)(x)` can be written as `f(g(x))`. I prefer the latter notation, because it better illustrates that you substitute the equivalent of `g(x)` for every x that you see in `f(x)`.

Explanation:

Given: `f(x)=x^2+7` and `g(x)=x-3`

To find `f(g(x))`, we substitute `x-3` for every x that we see in `f(x)`:

`f(g(x)) = (x-3)^2+7`

Technically, we are done but it is better to simplify the right side:

`f(g(x)) = x^2-6x+9+7`

`f(g(x)) = x^2-6x+16 larr` the answer