# Inverse function of inequality function

1. May 29, 2013

### xlu2

1. The problem statement, all variables and given/known data

Find inverse of each.
1. y<x+1
2. y=2x/(x-2)

2. Relevant equations
Switch y and x?

3. The attempt at a solution
For 1. I switched y and x, so x<y+1. Do I have to switch the sign also?
For 2. I switched y and x, so x=2y/(y-2). But I have to express the inverse function in terms of y. Is there another method I can use?

2. May 29, 2013

### DEvens

There's no such thing as an "inequality function." There are inequality relations. So there's no such thing as an inverse function of an inequality function. Your 1. is an inequality relation.

Also, your 2 is an equation, not an inequality at all.

By "switch y and x" it might be meant to manipulate the relations such that you get x isolated on one side of the relation, as compared to the starting condition where y is isolated on one side.

So, what operations can you perform on an inequality relation such that you keep the smaller side smaller and the larger side larger? For example, if you subtract 1 from each side, what happens?

9 < 10, then subtract 1, you get 8 < 9.

Your 2. is an equation. (Should the = sign be a < sign?) Does it mean, solve for x? Do you know how to do that?
Dan