**1. The problem statement, all variables and given/known data**

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

Find: [tex] f \circ g [/tex] and [tex] g \circ f [/tex]

**2. The attempt at a solution**

[tex] f \circ g =f(g(x))=x+2 [/tex], where [tex] x\in (-\infty ; +\infty) [/tex]

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

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