Math 3 function

Question

If f(x)=(x-5)^2 for x>5 then f^-1(x)=

Answer 1

f(x) = (x-5)² and x > 5. Then y = f(x) > 0.

Find f^-1(x):

y = (x-5)²

Switch x and y: x = (y-5)²

Solve for y:

Since the domain of f(x) is (5, ∞), the range of f^-1(x) is also (5, ∞). That is y - 5 > 0.

y - 5 = √x

y = f^-1(x) = 5 +√x