Question

is the inverse a function?
$h(x) = \sqrt{x + 7}$
yes
no

Explanation:

Step1: Find inverse of $h(x)$

Let $y = \sqrt{x+7}$. Swap $x$ and $y$: $x = \sqrt{y+7}$. Square both sides: $x^2 = y + 7$. Rearrange to solve for $y$: $y = x^2 - 7$.

Step2: Verify if inverse is a function

Use vertical line test: For any $x$-value in the domain ($x\geq0$ for the inverse, since original range is $y\geq0$), there is exactly one $y$-value.

Answer:

yes