Question

If f(x)=4[x-1] and g(x)=x+1, how do you find f(g(-1))?

Answer 1

`f(g(-1)) = -4`

Explanation:

When you have an expression:
`f(y)` ,
this means that you should plug in whatever `y` is into `x` in the function `f(x)`. That is, replace every instance of `x` with `y`.

There are two ways to find `f(g(-1))`
The first is to solve from the inside out.

Plug in `-1` into `g(x)` to get `g(-1)`:
`g(x) = x+1`
`g(-1) = -1 +1`
`color(blue)(g(-1) = 0)`

Then, plug in `g(-1)` into `f(x)`:
`f(x) = 4[x-1]`
`f(g(-1)) = 4[0-1]`
`color(blue)(f(g(-1)) = -4)`

The second way is to get `f(g(x))` first, then plug in `-1`:

`color(red)(f(x) = 4[x-1])`
`color(blue)(g(x) = x+1)`

`color(red)(f(color(blue)(g(x)))) = color(red)(4[color(blue)(x+1)-1])`

Then, you can plug in `-1`

`f(g(-1)) = 4[-1 +1 -1]`
`color(blue)(f(g(-1)) = -4)`