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 $g(x)=\sqrt{x+3}$
$y=\sqrt{x+3}$
$x=\sqrt{y+3}$ //Note here, $x\geq-3$
$x^2=y+3$
$y=x^2-3$
$g^{-1}(x)=x^2-3$
(b) We can sketch the graph of these functions using graphing calculator. See the image above.
