Answer
Domain Restriction: $[0,\infty)$
Inverse function: $f^{-1}(x)=x$
Work Step by Step
The Horizontal Line Test states that when all the horizontal lines intersect the graph function at no more than one point then the function is said to be one-to-one.
If a function $f(x)$ is one-to-one then for all $y=f(x)$ there is only one corresponding value of $x$.
The domain of the function $f(x)$ becomes the range of its inverse function and while the range of $f(x)$ becomes the domain of its inverse function $f^{-1}(x)$.
We can restrict the domain of the function $f(x)=|x|$ to $[0, \infty)$.
Since $x$ is non-negative, then
$$f(x) = |x| \implies f(x)=x$$
The graph of the inverse of a function is its reflection about the line $y=x$.
Since the function is $f(x)=x$, which is equivalent to $y=x$, then reflecting it about the $y=x$ line yields the same graph.
Thus, the inverse of $f(x)=x$ is itself.
