1. ## Composition of Functions

Hello everyone,

I'm having trouble finding the sums of functions.

My particular problem is,

They're asking me to solve (f+g)(x).

If (f+g)(x) is the same thing as f(x)+g(x) then:
(x-2)+?

Can x2/x2+1 be simplified so I can add the two functions easier?

I tried simplifying a bunch of things but I can't seem to get anywhere.
Any help would be appreciated. Thanks in advance!

2. $(f+g)(x) = f(x) + g(x)$

$(f \circ g)(x) = f[g(x)]$

3. I'm not sure how your functions look but I'm going to assume it was like this and you just forgot to indicate it was up to a power. Correct me if I'm wrong.

$f(x)=\sqrt{x^2-4}$

$g(x)=\frac{x^2}{x^2+1}$

so

$(f+g)(x) = f(x) + g(x)$

$= \sqrt{x^2-4} + \frac{x^2}{x^2+1}$

find common denominator

$= \frac{(x^2+1)\sqrt{x^2-4} + x^2}{x^2+1}$