MathDB

Let

\mathbb{R^+}

denote the set of positive real numbers. Assume that

f:\mathbb{R^+} \to \mathbb{R^+}

is a function satisfying the equations: f(x^3)=f(x)^3 \text{and} f(2x)=f(x) for all

x \in \mathbb{R^+}

. Find all possible values of

f(\sqrt[2022]{2})

1