Question

For the function f(x)=(8-2x)^2, find f^-1. Determine weather f^-1 is a function.

Answer 1

To get the inverse, what you'll do is:
(1) let f(x)=y, and replace x with y and y with x:
f(x) = (8 - 2x)^2
y = (8 - 2x)^2
x = (8 - 2y)^2

(2) solve for y, and substitute back the y=f(x):
x = (8 - 2y)^2
sqrt(x) = 8 - 2y
sqrt(x) - 8 = -2y
y = (sqrt(x) - 8) / (-2)
y = (8 - sqrt(x)) / 2
f(x) = (8 - sqrt(x)) / 2

hope this helps~ `u`