Answer
$1\leq x$, $g^{-1}(x)=\sqrt{x}+1$.
Work Step by Step
To make the function one-to-one, according to the graph, we can restrict its domain to $1\leq x$. If we want to get a formula for the inverse function, we swap $x$ and $y$ and solve for $y$. Hence, after swapping $x$ and $y$, we get:
$x=(y-1)^2\\\sqrt x=y-1\\y=g^{-1}(x)=\sqrt{x}+1$.
