I need help with an inverse function. If f(x)=3-x, I find the inverse function to be: x=3-y which is the same as y=3-x, same as the original. How can this be?

Answer 1

Did you realize that
f(x) = 3-x is the same as
x + y = 3 ?

Step one in finding the inverse is to interchange the x and y variables, and lo and behold you would get
y + x = 3, which of course is the same as the one you started with.

Another explanation:
After finding the inverse, the resulting graph is a reflection in the line y = x
graph y = 3 - x, and you will see that reflecting it in the line y = x yields the same line.

Answer 2

Thanks!