### Home > INT3 > Chapter 8 > Lesson 8.3.1 > Problem8-96

8-96.

What is the inverse of g(x) = (x + 1)2 – 3 for x ≥ –1? Sketch graphs of g(x) and its inverse on the same set of axes, and then state the domain and range of the inverse function. Homework Help ✎

Let g(x) = y. Then interchange x and y.
x = (y + 1)2 − 3

Add 3 to both sides of the equation.
x + 3 = (y + 1)2

Take the square root of both sides.

$y + 1 = \sqrt{x + 3}$

$g^{-1}(x) = \sqrt{x + 3} - 1$

D: x ≥ −3
R: y ≥ −1