Foggy Dirichlets

Algebra Level 3

The functions f(x)f(x) and g(x)g(x) are defined R+R\mathbb {R^+ \to R} such that f(x)={1xx is rationalx2x is irrationalg(x)={x   x is rational1xx is irrationalf(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 fg(x)f \circ g(x) is

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