Question

question 2 of 10 step 1 of 2 consider the following function on the given domain. \\( a(x) = (x + 3)^2 - 3, x \geq -3 \\) step 1 of 2: find a formula for the inverse of the function on the given domain, if possible. answerhow to enter your answer (opens in new window) 2 points selecting a radio button will replace the entered answer value(s) with the radio button value. if the radio button is not selected, the entered answer is used. \\( a^{-1}(x) = \\) \\( \bigcirc \\) does not have an inverse fun

Explanation:

Step1: Set $y = A(x)$

$y = (x + 3)^2 - 3, \ x \geq -3$

Step2: Swap $x$ and $y$

$x = (y + 3)^2 - 3, \ y \geq -3$

Step3: Solve for $y$

Add 3 to both sides:
$x + 3 = (y + 3)^2$
Take square root (since $y \geq -3$, $y+3 \geq 0$, we use positive root):
$\sqrt{x + 3} = y + 3$
Subtract 3 from both sides:
$y = \sqrt{x + 3} - 3$

Step4: Replace $y$ with $A^{-1}(x)$

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

Answer:

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