Foggy Dirichlets

Algebra Level 3

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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