To find the inverse of a function, you can follow these steps:
Swap the variables x and y in the original function. For example, if the original function is y = √x + 8, you would swap the variables to get x = √y + 8.
Solve the equation for y. In this case, you would get:
x = √y + 8
y = x - 8
Replace y with f^-1(x) to denote the inverse function. The inverse function is defined as f^-1(x) = y, so you would get:
f^-1(x) = x - 8
This is the inverse function of y = √x + 8.
Note that the inverse function is only defined for values of x such that y ≥ 8. This is because the original function y = √x + 8 is only defined for y ≥ 8.