Answer
Sample answer:
$f^{-1}(x)=\sqrt{x}+3, \quad x\geq 0$
(see "step by step" for details)
Work Step by Step
The graph is symmetric about the line x=3.
As is now, it fails the Horizontal line test.
[ f(2)=f(4)=1 ]
If we reduce the domain to $x\leq 3$ or $x \geq 3$, (either side of the axis of symmetry)
the graph will pass the test (become one-to-one).
The domain may be reduced in many ways:
$x\leq 2, x\leq 1,....$ or x$\geq 4, x\geq 5$, etc.
We select, as a sample answer,$ x \geq 3.$
To find the inverse,
1. swap f(x)=y and x:
$y=(x-3)^{2}, \quad x \geq 3, y\geq 0$
$x=(y-3)^{2}, \quad y \geq 3, x\geq 0$
2. Solve for y:
$\sqrt{x}=y-3\qquad /+3$
$\sqrt{x}+3=y, \quad $
$y=\sqrt{x}+3, \quad x\geq 0$
3. Replace $y $ with $f^{-1}(x):$
$f^{-1}(x)=\sqrt{x}+3, \quad x\geq 0$
