### Home > A2C > Chapter 9 > Lesson 9.3.2 > Problem9-144

9-144.

Find the inverse of $g\left(x\right) = \left(x + 1\right)^{2} − 3$ with the domain $x ≥ −1$. Sketch both graphs and tell the domain and range of the inverse function.

First switch the placement of $x$ and $y$.

$x = \left(y + 1\right)^{2} − 3$

$x + 3 = \left(y + 1\right)^{2}$

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

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

$\text{D}: x ≥ −3, \\\text{R}: y ≥ −1$