CPM Homework Help : CCA2 Problem 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.

Step 1:

Let $g(x) = y$ . Then interchange $x$ and $y$ .
$x = (y + 1)^2 - 3$

Step 2:

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

Step 3:

Take the square root of both sides. $y+1=\sqrt{x+3}$

Answer:

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