Answer
$ a.\quad$The graph is symmetric about the line $y=x.$
$b.\quad f(x)=f^{-1}(x)$
Work Step by Step
$a.$
See graph.
The graph is symmetric about the line $y=x.$
$b.$
Solve the equation for x, writing $y=f(x)$
$ y=\sqrt{1-x^{2}} \qquad$... square both sides, note that $x\geq0,y\geq 0$
$ y^{2}=1-x^{2} \qquad$... add $x^{2}-y^{2}$
$ x^{2}=1-y^{2}\qquad$... take the square root
$ x=\pm\sqrt{1-y^{2}}\qquad$... interchange $x\leftrightarrow y$, and apply $x,y\geq 0$
$y=f^{-1}(x)=\sqrt{1-x^{2}}=f(x)$
