The correct answer is D.
In order to solve for a function's inverse, you must start by switching the x and f(x) values. Then you solve for the new f(x). Once you have done that, you'll be left with the new function, which is the inverse of the original. See the work below for how this one will be solved.
f(x) = [tex] \sqrt{x - 1} + 5 [/tex] ----> Switch the x and f(x)
x = [tex] \sqrt{f(x) - 1} + 5 [/tex] ----> Now subtract the 5 from both sides.
x - 5 = [tex] \sqrt{f(x) - 1} [/tex] ---> Now square both sides.
[tex] (x-5)^{2} [/tex] = f(x) - 1 ----> Now add 1 to both sides.
[tex] (x-5)^{2} [/tex] + 1 = f(x)
And now that you have something equaling f(x), you can change the order and match it up to answer D.
f(x) = [tex] (x-5)^{2} [/tex] + 1
