The quantile function of $X$ is the D4364: Real function
\begin{equation}
[0, 1] \to \mathbb{R}, \quad
x \mapsto \inf \left\{ t \in \mathbb{R} : x \leq F(t) \right\}
\end{equation}
Let $X \in \text{Random}(\mathbb{R})$ be a D3161: Random real number.
The quantile function of $X$ is the D4364: Real function
\begin{equation}
[0, 1] \to \mathbb{R}, \quad
x \mapsto \inf \left\{ t \in \mathbb{R} : x \leq \mathbb{P}(X \leq t) \right\}
\end{equation}