Answer
(a) $g^{-1}(x)=x^2-3$
(b) See the image below.
Work Step by Step
(a) To find inverse of the function we have to follow the next strategy:
First write down the function in terms of $y$ and $x$,
Then replace $y$ by $x$ and vice versa,
At last solve the equation for $y$.
We have $g(x)=x^2+1$, $x\geq0$
$y=x^2+1$
$x=y^2+1$
$y^2=x-1$
$y=\sqrt{x-1}$
$g^{-1}(x)=\sqrt{x-1}$ ; $x\geq0$
(b) We can graph both of these functions using graphing calculator. See the image above.
