Composition of two functions - Precalculus question?

Question

abbles · Answer

Express the following function, F(x), as a composition of two functions, f and g: f(g(x)).

$$F(x) = x^2/(x^2 + 4)$$

abbles · Answer

Part 1: What function is g(x)?

abbles · Answer

Part 2: What function is f(x)?

agent0smith · Answer

There's multiple correct answers here. Here's one 

g(x) = x^2

f(x) = x/(x+4)

abbles · Answer

Thanks!

jim_thompson5910 · Answer

Here's another, but it's probably not what your teacher would want

f(x) = x
g(x) = (x^2)/(x^2+4)
F(x) = (f o g)(x) = (x^2)/(x^2+4)

agent0smith · Answer

What do you get when you find f(g(x)) for the two functions i gave? Make sure it gives you the correct function.

abbles · Answer

@jim_thompson5910  Ha!

agent0smith · Answer

@jim_thompson5910 that one's fine too imo.

abbles · Answer

So I plug "x^2" into x/(x+4) in place of x, right? Pretty straightforward.  I understand the concept, was just having a blank moment I suppose

abbles · Answer

Thanks for the help.

agent0smith · Answer

Exactly, that's what you do.