[Math] Continuous function with no fixed point

Question

I am searching an example of a continuous function $f: [0,1) \to [0,1)$ but f has no fixed point, that is, there is no point $x_0 \in [0,1)$ such that $f(x_0)\not= x_0 \forall x_0$.

Answer 1

Hint: consider polynomials of degree $1$ such that $f(1)=1$.