Question

If `f(x)=x^2+4x` and `g(x)=3x-5`, how do you find `(f(g(x))` and `g(f(x))`?

Answer 1

It might be better if we think of the functions as having different parameters, so

If `f(a)=a^2+4a`
and `g(b)=3b−5`,

then
`f(g(x))` simply means re-writing the `f(a)` equation with `a` replaced by `g(x)`:
`f(g(x))`
`= (g(x)^2 + 4(g(x))`
`= (3x - 5)^2 + 4(3x -5)`
`= 9x^2 -18x +5`

Similarly
`g(fx))`
`= 3(x^2 + 4x) - 5` (by replacing `b` with `f(x)`)
`= 3x^2 + 12x`