Question

What is the inverse of the function​

Answer 1

Answer:

$x^2-10x+31$

Step-by-step explanation:

$y=\sqrt{x-6}+5$

$x=\sqrt{y-6}+5$

$\sqrt{y-6}+5=x$

$\sqrt{y-6}+5-5=x-5$

$\sqrt{y-6}=x-5$

$\left(\sqrt{y-6}\right)^2=\left(x-5\right)^2$

$\left(\sqrt{y-6}\right)^2$

$=\left(\left(y-6\right)^{\frac{1}{2}}\right)^2$

$=y-6$

$\left(x-5\right)^2$

$=x^2-10x+25$

$y-6=x^2-10x+25$

$y-6+6=x^2-10x+25+6$

$y=x^2-10x+31$