My friend has given me a math problem to solve just for fun. I have never seen these types of functions before but I undrestand what composition means.
If $f(x)=\left\{ \begin{array}{ll} 1+x, & \hbox{when }x<0 \\ 2 & \hbox{when }x>0 \end{array} \right.$ and $g(x)=\left\{ \begin{array}{ll} -1, & \hbox{when }x<1; \\ x, & \hbox{when }x\geq 1 \end{array} \right.$
How would I go about finding the formula of $g\circ f$ (composition of $g$ and $f$)?