Question 729300
The question seems to ask you for what would be the upper branch of the resulting inverse, which is why the condition, {{{x<=4}}}.


Assume you will call the inverse of f(x), as g(x).  You want g(f(x))=f(g(x))=x.


Starting with your given function, f(x), {{{f(g(x))=((g(x))-4)^2}}} and you must have {{{((g(x)-4))^2=x}}}.
{{{g(x)-4=sqrt(x)}}}, and we will use this positive root, not the negated root.
{{{highlight(g(x)=sqrt(x)+4)}}}, the inverse of f(x).


As for the domain of g(x), just ask yourself, what is the set of numbers which is acceptable for x?