First, we need to find the inverse of our function [tex]f(x)= \sqrt{x-4} [/tex]. To do that we are going to take advantage of the fact that [tex]f(x)=y[/tex]. So we can rewrite our function as [tex]y= \sqrt{x-4} [/tex]; now, we are gong to interchange [tex]x[/tex] and [tex]y[/tex] and solve for [tex]y[/tex] to find our inverse:
[tex]y= \sqrt{x-4} [/tex]
[tex]x= \sqrt{y-4} [/tex]
[tex] x^{2} =y-4[/tex]
[tex]y= x^{2} +4[/tex]
Since this is the parabola [tex] x^{2} [/tex] shifted 4 units upwards. Its range will be [4,∞)
