Question

What is the domain and range of the inverse of: f (x)= (x + 2)² - 1

Answer 1

The inverse of this function is a parabola that has been rotated 90 degrees clockwise, with it's vertex at point 1, 0.

So it's domain is x ≥ 1

And it's range is y ≥ -2

Explanation:

Given:

f(x) = (x + 2)² - 1

First we find the inverse:

x = (f(x) + 2)² - 1

x - 1 = (f(x) + 2)²

√(x - 1) = f(x) + 2

f(x) = -2 ± √(x - 1)