Question

Select the correct answer. Which function is the inverse of f(x) = x² - 16 if the domain of f(x) is x ≥ 0?

f-¹ (x)=√x+16
f-¹ (x) =√x+4
f-¹ (x) = √x-16
f-¹ (x) = √x-16​

Answer 1

The inverse of the function f(x) = x² - 16, with the domain x ≥ 0, is given by f-1(x) = √x + 16.

Step-by-step explanation:

The inverse of the function f(x) = x² - 16, with the domain x ≥ 0, can be found by following these steps:

1. Replace f(x) with y, so the equation becomes y = x² - 16
2. Switch the roles of x and y, giving you x = y² - 16
3. Replace x with the given x-value, in this case x = √x + 16
4. Solve the equation for y by isolating it on one side

Therefore, the correct answer is f-1(x) = √x + 16.