I have the function:
f: [0,2] to R defined by
f(x)=x for 0 less than or equal to x less than or equal to 1
f(x)=1+x for 1 less than x less than or equal to 2

Just by graphing, I know that this is strictly increasing on [0,2] but would could I prove it?

Also, I need to find the points of discontinuity for this function and its inverse.
For f, it would be y=1.
For inverse f, it would be x=1. Is this right?