Question

Which function represents the inverse of f(x) = √x + 5?

A: f^-1(x) = (x + 5)^2, x ≥ −5
B: f^-1(x) = x^2 - 5, x ≥ 0
C: f^-1(x) = (x - 5)^2, x ≥ 5
D: f^-1 (x) = x^2 + 5, x ≥ 0

Answer 1

To find the inverse function, we want to replace f(x) with y and then solve for x.

Starting with f(x) = √x + 5, let's replace f(x) with y:
y = √x + 5

Next, let's switch the roles of x and y:
x = √y + 5

Now, let's isolate √y:
√y = x - 5

To get rid of the square root, we will square both sides of the equation:
(√y)^2 = (x - 5)^2
y = (x - 5)^2

Therefore, the inverse function is f^-1(x) = (x - 5)^2.

The correct option is C: f^-1(x) = (x - 5)^2, x ≥ 5.