Cancellation propriety for continuous functions.

Cancellation propriety for continuous functions.

Let's say we have a continuous function $f:\mathbb{R}^n \rightarrow
\mathbb{R}^n$ such that there exist $k,s \in \mathbb{N}: f^k=f^s$. Is it
true that $f^{|k-s|}=id$? Is it true something similar?