Question

Given the function below, is the inverse a function? How do you know?

f(x) = (x – 4)²
A) Yes, this function fails the horizontal line test.
B) No, this function fails the horizontal line test.
C) No, this function passes the horizontal line test.
D) Yes, this function passes the vertical line test.

Answer 1

The inverse of the function f(x) = (x – 4)² is a function that passes the horizontal line test.

Step-by-step explanation:

Given the function f(x) = (x – 4)², we need to determine if its inverse is a function. To find the inverse of a function, we need to switch the roles of x and y and solve for y. Let's do that:

y = (x – 4)²

Switching the x and y:

x = (y – 4)²

To solve for y, we need to take the square root of both sides:

√x = y – 4

y = √x + 4

Since we obtained a unique y-value for every x-value, the inverse of f(x) is indeed a function. Therefore, the answer is C) No, this function passes the horizontal line test.