Onto of compositions of onto functions when function is define

Question

Suppose we have two functions, $f:\mathbb{R} \rightarrow \mathbb{R}$ by $f(x) = 2x - 3$ $g:\mathbb{R} \rightarrow \mathbb{R}$ If both of these functions are onto, how can we show that $g\circ f:\mathbb{R}\rightarrow \mathbb{R}$ is onto?

$ f: X \rightarrow Y$ onto means $$\forall y \in Y, \exists x \in X \text{ such that } f(x) = y$$

Answer 1

Show h:R -> R is onto iff h(R) = R.
To show gf is onto, show gf(R) = g(R) = R.