Commutative Diagram/Examples/Square Function with Square Root

Example of Commutative Diagram
Let $g$ and $h$ be the real functions defined as:


 * $\forall x \in \R: \map g x = x^2$


 * $\forall x \in \R_{\ge 0}: \map h x = \sqrt x$

The composition $h \circ g$ can be depicted using a commutative diagram as follows:


 * $\begin{xy} \xymatrix@L+2mu@+1em{

\R \ar[r]^*{g} \ar@{-->}[rd]_*{h \circ g} & \R_{\ge 0} \ar[d]^*{h} \\ & \R_{\ge 0} }\end{xy}$