I have no idea how to do this?
Q: Give an example of an increasing function with the set of all real numbers as its domain and codomain that is not one-to-one?
I think one simple example would be the function $\displaystyle f:R \rightarrow R$ defined by $\displaystyle f(x)=x^2$. This function is increasing on $\displaystyle R^+$, and clearly is not one-to-one since you can have $\displaystyle f(a)=f(-a)=a^2$ where $\displaystyle a \in R$, contradicts the definition of being one-to-one.