If f is surjective and g is injective, what is $f\circ g$ and $g\circ f$? Say I have $f=x^2$ (surjective) and $g=e^x$ (injective), what would $f\circ g$ and $g\circ f$ be? (injective or surjective?)
Both $f$ and $g : \mathbb{R} \to \mathbb{R}$.
I've graphed these out using Maple but I don't know how to write the proof, please help me!

When you write $x$ in $f(x)=x^2$, it is a "dummy variable" in that you can put in anything in the proper range (here presumably the real numbers).  So $f(g(x))=(g(x))^2$.  Then you can expand the right side by inserting what you know about $g(x)$.  Getting $g(f(x))$ is similar.  Then for the injective/surjective part you could look at this question
