Question

find the inverse for the function $y=(x-4)^2+2$

Explanation:

Step1: Swap x and y variables

$x = (y - 4)^2 + 2$

Step2: Isolate the squared term

$x - 2 = (y - 4)^2$

Step3: Take square root of both sides

$\pm\sqrt{x - 2} = y - 4$

Step4: Solve for y

$y = 4 \pm \sqrt{x - 2}$

Step5: Define domain of inverse

For the square root to be real, $x - 2 \geq 0 \implies x \geq 2$

Answer:

$y = 4 \pm \sqrt{x - 2}$ where $x \geq 2$