I'm trying to make sure I got this question right. I'm supposed to find (g * f)(x) when f(x)x^2-2x and g(x)=√(x-15).

Question

This is what I've got:
(g * f)(x) = g(f(x))

√ (x^2-2x)-15=
√(x^2-2x-15)=
√(x-5)(x+3)

Answer 1

Hmmm.

(g*f)(x) = g(x)*f(x)
= √(x-15)(x^2-2x)

The composite function

(g◦f)(x) = g(f(x))
= √(f-15)
= √(x^2-2x-15)

Your factoring is correct, but I see no advantage to it. It ought also to be written as √((x-5)(x+3)) to avoid confusion with

√(x-5) * (x+3)

since usually parentheses delimit arguments of functions.

Answer 2

Alright, so if the question is asking for a * then I multiply both functions together, but if its asking for a ◦ then I plug in one function the the other?
ps,
Thanks for your help!