Question

question 2 of 10 step 2 of 2 consider the following function on the given domain. \\( a(x) = (x + 3)^2 - 3, x \geq -3 \\) step 2 of 2: find the domain of the inverse function, \\( a^{-1}(x) \\). express your answer as an inequality. answer 2 points keypad keyboard shortcuts

Explanation:

Step1: Identify range of original function

For $A(x)=(x+3)^2-3$ with $x\geq-3$:
Let $t=x+3$, so $t\geq0$. Then $A(x)=t^2-3$. Since $t^2\geq0$, $t^2-3\geq-3$. So range of $A(x)$ is $y\geq-3$.

Step2: Relate inverse domain to original range

The domain of the inverse function $A^{-1}(x)$ is equal to the range of the original function $A(x)$.

Answer:

$x\geq-3$