Home > CCA2 > Chapter 8 > Lesson 8.3.2 > Problem8-142

8-142.

Find the inverse of $g(x) = (x + 1)^2 - 3$ with the domain $x ≥ -1$. Sketch both graphs and state the domain and range of the inverse function.

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. $y+1=\sqrt{x+3}$

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