How do you find the inverse of f(x)=3+sqrt(x-8)f(x)=3+x8?

1 Answer
Jun 5, 2015

Answer: The inverse function is f(x)=x^2-6x+17f(x)=x26x+17

Explanation: We have the equation y=3+sqrt(x-8)y=3+x8.

In order to find the inverse function, we have to switch the variables xx and yy and then solve for yy:

x=3+sqrt(y-8)x=3+y8 => sqrt(y-8)=x-3y8=x3 => y-8 = (x-3)^2y8=(x3)2 => y= (x-3)^2 +8y=(x3)2+8 => y=x^2-6x+17 y=x26x+17