# Math Help - Functions

1. ## Functions

How we prove in a function f that f(R)=R?
By proving that is '1-1'?

2. If $f:\mathbb{R}\to\mathbb{R}$, i.e., it is declared that the domain and the codomain of $f$ are $\mathbb{R}$, then the claim that $f(\mathbb{R})=\mathbb{R}$ means that $f$ is surjective. On the other hand, the fact that $f$ is 1-1 means that it is injective. These are different concepts; none of them implies the other. For example, for $f(x)=x^3-x$ we have $f(\mathbb{R})=\mathbb{R}$, but $f$ is not 1-1.

3. thank you man