Let f and g be paths in R. Show that f is homotopic to g.

Question

Question:

Let $f$ and $g$ be paths in $\mathbb R$. Show that $f$ is homotopic to $g$.

Answer:

Does the homotopy $F(x,t)=tf(x)+(1-t)g(x)$ is a proof for the statement?

Answer 1

Community wiki answer so the question can be marked as answered:

As noted in the comments, this is a correct homotopy. It proves that $f$ is homotopic to $g$.