Question

question 4 of 10 step 2 of 2
00:51:21
consider the following function on the given domain.
$a(x) = (x + 1)^2 + 3, x \geq -1$
step 2 of 2: find the domain of the inverse function, $a^{-1}(x)$. express your answer as an inequality.
answer 2 points

Explanation:

Step1: Find range of $A(x)$

For $x\geq -1$, let $t=x+1$, so $t\geq0$. Then $A(x)=t^2+3$. Since $t^2\geq0$, $t^2+3\geq3$.

Step2: Relate range to inverse domain

The domain of $A^{-1}(x)$ equals the range of $A(x)$.

Answer:

$x\geq 3$