Answer
See graph and explanations.
Work Step by Step
Step 1. Graph the function $y_1=\sqrt {2-x}$ as the blue curve in the figure.
Step 2. Graph the function $y_2=\sqrt x$ as the green curve in the figure.
Step 3. Graph the composite function $y_3=\sqrt {2-y_2}$ as the red curve in the figure.
Step 4. We can identify the domain of $f\circ g$ as $[0,4]$
Step 5. Algebraically, we have $f\circ g=\sqrt {2-\sqrt x}$ and the domain requirement is that $2-\sqrt x\geq0$ which requires $0\leq x\leq 4$ or $[0,4]$
