Yep... Thats a good way to do it. You know it is invertible if f(x)=f(y) implies x=y. What this means is, if you can draw a horizontal line anywhere on the x-y plane, and only hit the graph of f once, it is invertible. If any horizontal line hits it more than once, than you need to break it up into several functions (each over its own part of the domain), so that the horizontal line test mentioned above is satisfied. Try this on y=abs(x - 6), and see at what x value you need to break the function to achieve this.
I hope this undoes any confusion I caused earlier.
