Question

4 multiple choice 1 point a function is defined by $y = \sqrt{x - 4}$. what function represents the inverse of this function? $\bigcirc$ $y = x^2 + 4; x \geq 0$ $\bigcirc$ $y = x^2; x \geq 4$ $\bigcirc$ $y = x^2 - 4; x \geq 0$ $\bigcirc$ $y = \sqrt{x + 4}$

Explanation:

Step1: Swap x and y variables

$x = \sqrt{y - 4}$

Step2: Square both sides to eliminate root

$x^2 = y - 4$

Step3: Solve for y

$y = x^2 + 4$

Step4: Define domain of inverse

Original function $y=\sqrt{x-4}$ has range $y\geq0$, so inverse domain is $x\geq0$.

Answer:

$y = x^2 + 4; x \geq 0$