Let f(x)=square root(x-4) + 3 . Find the inverse of f.

To determine the inverse of the function, we'll re-write
the function, putting instead of f(x), y:

y = sqrt(x-4) +
3

We'll interchange x and y:

x
= sqrt(y-4) + 3

We'll determine y from the expression
above. We'll subtract 3 both sides:

x - 3 =
sqrt(y-4)

We'll raise to square both
sides:

(x-3)^2 = y - 4

We'll
add 4 both sides and we'll apply symmetrical property:

y =
(x-3)^2 + 4

The inverse function of f(x) is
f^-1(x) = (x-3)^2 + 4.