TITLE: Injective function that is not surjective
QUESTION [8 upvotes]: I'm trying to find an example of a continuously differentiable function from $\mathbb{R}$ to $\mathbb{R}$ that is injective but not surjective. 
I can easily find one from $\mathbb{Z}$ to $\mathbb{Z}$ but I'm having difficulty finding one for the reals.

REPLY [34 votes]: Hint: It might be easier than expected.