Is the functions $f+g$ one to one?

Question

I am reviewing for a test and there is this question.

Functions $f: \mathbb R\to \mathbb R$, $g: \mathbb R\to\mathbb R$ are both one to one on the set of real numbers $\mathbb R$. Is the function $f + g$ also one to one? Prove your answer.

So to prove one to one, you need to find two distinct elements of $X$ that have distinct images of $Y$. I am not sure what $f+g$ is even supposed to be. Is it $(f\circ g)=f(g(x))$? How would can I think of this problem to prove it? by example maybe?

Answer 1

Presumably, $(f + g)(x) = f(x) + g(x)$. Consider the case $f = -g$.

Answer 2

Let $f(x)=x$ and let $g(x)=-x^3$, both $R\to R$ and one to one. However $h=x-x^3$ has 3 zeros, and therefore cannot be one to one. To clarify it $h(1)=h(0)$, but $0\ne 1$.