Question

what is the inverse of: f(x) = 2(x – 4)^2 + 5

Answer 1

y = 2(x-4)^2 + 5
(y-5)/2 = (x-4)^2
If we take the square root, there are two branches. Let's take the + branch:

sqrt((y-5)/2) = x-4
x = 4 + sqrt((y-5)/2)

so, f^-1(x) = 4 + sqrt((x-5)/2)

technically, f has no inverse, since there is not a unique value of x for each value of y.