Let K be a subset of R
A function F: K--> R is said to be strictly monotonic if it is either strictly increasing or strictly decreasing. That is, one of the following 2 holds:
1.) x,y are elements in K with x<y implies that f(x)<f(y)
2.) x,y are elements in K with x<y implies that f(x)>f(y)
Let I be an interval in R and let f: I-->R be a continuous function.
Prove that f is one-to-one iff f is strictly monotonic.
I am having trouble starting this problem and any help would be much appreciated.