Answer
a) $f^{-1}(x)=3-x^2$
b) see graph
Work Step by Step
To find the inverse of a function, one must swap places of $x$ and $f(x)$ and then solve for $f(x)$
$f(x)=\sqrt{3-x}$ Swap places
$x=\sqrt{3-f(x)}$ Solve for $f(x)$ by first squaring both sides
$x^2=(\sqrt{3-f(x)})^2$
$x^2=3-f(x)$ Add $f(x)$ to both sides and subtract $x^2$ from both sides as well
$x^2+f(x)-x^2=3-f(x)+f(x)-x^2$ Simplify
$f(x)=3-x^2$
Since the range of the original function is [0, ∞), the domain of the inverse function is [0, ∞) as it appears on the graph.