What is the inverse function of #y=2-x#?

1 Answer
Nov 25, 2015

#y=2-x#

Explanation:

How to find an inverse function:
Flip the position of #x# and #y#.
Solve the equation in terms of #y#.

If we start with #y=2-x#, we must first flip #x# and #y#.

This gives us:

#x=2-y#

Then, we have to solve for #y#.

Subtract #2# from both sides:

#x-2=-y#

Multiply both sides by #-1#.

#y=-x+2#

This is the inverse function of #y=2-x#.

(Fun fact: this function's inverse is itself! In linear functions, this happens when there's a slope of #-1#.)