If (f:\mathbb{R}\to \mathbb{R}) and (g:\mathbb{R}\to \mathbb{R}) are both onto, what is the correct statement about (g\circ f)?

Correct answer: (g\circ f) is onto

Step 1: Since (g) is onto, for every target (y), there is some (u) with (g(u)=y). Step 2: Since (f) is onto, for that (u), there is some (x) with (f(x)=u). Step 3: Therefore (g(f(x))=y), so the composition is also onto.