Which answer choice represents the inverse of f(x) = √x - 7?

Question

A: f^-1(x) = x^2 - 7, x ≥ 0
B: f^-1(x) = x^2 + 7, x ≥ 0
C: f^-1(x) = (x - 7)^2, x ≥ 7
D: f^-1(x) = (x + 7)^2, x ≥ -7

Answer 1

To find the inverse of a function, we switch the roles of x and y and solve for y. So, let's switch x and y in the original function:

x = √y - 7

Now, let's solve for y:

x + 7 = √y

(x + 7)^2 = y

Therefore, the inverse function is:

f^-1(x) = (x + 7)^2

The answer choice that represents this is option D: f^-1(x) = (x + 7)^2, x ≥ -7.