Strictly increasing functions/Doubling per step/Not 2^x/Exercise

Give an example of a continuous, strictly increasing function

$f\colon \mathbb {R} \longrightarrow \mathbb {R} _{+}$

fulfilling ${}f(0)=1$ and ${}f(x+1)=2f(x)$ for all ${}x\in \mathbb {R}$,

which is different from ${}2^{x}$.

Create a solution