Question

10 multiple choice 1 point what is the inverse of the given function? $y=(x + 3)^2; xgeq - 3$ $y=sqrt{x}-3$ $y=sqrt{x}+3$ $y=x^2 - 3$ $y=sqrt{x + 3}$

Explanation:

Step1: Swap x and y variables

$x = (y + 3)^2$

Step2: Solve for y (take square root)

$\sqrt{x} = y + 3$

Step3: Isolate y

$y = \sqrt{x} - 3$

Step4: Verify domain/range

Since original $x\geq-3$, inverse $y\geq-3$, which matches $\sqrt{x}-3$ (as $\sqrt{x}\geq0$, so $\sqrt{x}-3\geq-3$)

Answer:

A. $y = \sqrt{x} - 3$