Composition of Functions (check me)

[Lynne]

Hi,

Homework Statement

Given:f(x)=x^2+2 and g (x)=\sqrt{x}

Find: f \circ g and g \circ f

2. The attempt at a solution
f \circ g =f(g(x))=x+2, where x\in (-\infty ; +\infty)

g \circ f =g(f(x))=\sqrt{x^2+2} where x\in (-\infty ;+ \infty)

I haven't done this for a while, and I'm not sure about my solution. Is it correct?

 

[Dick]

Almost. Except g(x) is only defined for x in [0,infinity).