Question

Given the function f(x) = (x - 13)^2, x ≤ 13, complete parts a through c, and find an equation for f^(-1)(x).

Answer 1

To find the equation for f^(-1)(x), we need to switch the roles of x and y in the original function f(x). The equation for f^(-1)(x) is y = √x + 13.

Step-by-step explanation:

To find the equation for f^(-1)(x), we need to switch the roles of x and y in the original function f(x). Let's start with the function f(x) = (x - 13)^2.

Step 1: Replace f(x) with y: y = (x - 13)^2.

Step 2: Swap x and y: x = (y - 13)^2.

Step 3: Solve for y:

1. Take the square root of both sides: √x = y - 13.
2. Add 13 to both sides: √x + 13 = y.

The equation for f^(-1)(x) is y = √x + 13.