The functions $f(x)$ and $g(x)$ are defined $\mathbb {R^+ \to R}$ such that $f(x)=\begin{cases} 1-\sqrt{x}\quad \text{x is rational} \\ \quad x^2\quad\quad\text{x is irrational}\end{cases}\\g(x)=\begin{cases} \quad x\quad\quad~~~ \text{x is rational} \\ 1-x\quad\quad\text{x is irrational}\end{cases}$

The composite function $f \circ g(x)$ is

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