Discrete math functions (Onto, One-to-One) Proof

Discrete math functions (Onto, One-to-One) Proof

Let $f : \mathbb Z \to \mathbb Z$ and $g : \mathbb Z \to \mathbb Z$ be
functions defined by $f(x) = 3x + 1$ and $g(x) = \lfloor x/2\rfloor$ (this
is floor of x/2) for each $x\in\mathbb Z$
Is $g\circ f$ one-to-one? Prove your answer.
Is $g\circ f$ onto? Prove your answer.
Is $f\circ g$ one-to-one? Prove your answer.
Is $f\circ g$ onto? Prove your answer.