Define f:[0,1] → [0,1] by \(f(x)=\left\{\begin{array}{ll} 1 & \text { if } x=0, \\ \frac{1}{n} & \text { if } x=\frac{m}{n} \text { for some } m, n \in \mathbb{N} \text { with } m \leq n \text { and } \operatorname{gcd}(m, n)=1, \\ 0 & \text { if } x \in[0,1] \text { is irrational. } \end{array}\right.\) and define g:[0,1] → [0,1] by \(g(x)=\left\{\begin{array}{ll} 0 & \text { if } x=0 \\ 1 & \text { if } x \in(0,1] \end{array}\right.\) Then which of the following is/are true?
1
f is Riemann integrable on [0, 1].
2
g is Riemann integrable on [0, 1].
3
The composite function f ∘ g is Riemann integrable on [0, 1].
4
The composite function g ∘ f is Riemann integrable on [0, 1].