Since random numbers are generated for the uniform distribution $p(x)$ with $x\in [0,1]$, we need to perform a change of variables $x\rightarrow y$ through $$\begin{equation*} x(y)=\int_a^y p(y')dy', \end{equation*}$$ where we used $$\begin{equation*} p(x)dx=dx=p(y)dy. \end{equation*}$$ If we can invert $x(y)$, we find $y(x)$ as well.