meaning of the notation a belongs to $ C^n[a,b]$

Question

This notation stands for what : $X$ belongs to $C^n[a,b]$ ? I think $x$ takes values continuously between $a$ and $b$ in $n$ tuples.

Answer 1

Typically $C^n[a,b]$ denotes the set of all functions $f$, where $f$ is an $n$-times differentiable continuous function over the interval $[a,b]$.