Question

How do you find `g(f(x))` if `g(x) = x^2` and `f(x) = x + 3`?

Answer 1

Replace all `x`'s in `g(x)` with the function `f(x)` to get
`g( f(x) ) = ( x+3 )^2`

Explanation:

`g(f(x))` means that you replace all `x`'s in `g(x)` with the function `f(x)`. The easiest way to do this is rewrite `g(x)`, replacing all `x`'s with a blank set of parenthesis, like this -

`g( f(x) ) = ( )^2`

Now place the function `f(x)` into the parenthesis.

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