Question

How do you find `(fog)(n)` given `f(n)=2n` and `g(n)=-n-4`?

Answer 1

`(fog)(n)=-2n-8`

Explanation:

It is sometimes easier to thing of `(fog)(n)` as `f(g(n))`

It might also help to replace `n` in the definition of `f(n)` with some other variable; since `n` is just a variable placeholder there is no problem doing this.

So `f(n)=2n` could equally validly written as
`color(white)("XXX")f(color(red)k)=2color(red)(k)`

Now, if we want to evaluate `f(color(blue)(g(n)))`
we simply replace `color(red)(k)` with `color(blue)(g(n))`

`color(white)("XXX")f(color(blue)(g(n)))=2color(blue)(g(n))`

and since `color(blue)(g(n))color(black)=-n-4`
`color(white)("XXX")f(color(blue)(g(n)))=2(color(blue)(-n-4))=-2n-8`