If (f:\mathbb{R}\to\mathbb{Z}) is defined by (f(x)=\lfloor x\rfloor), which statement about (f) is correct?

Correct answer: Onto but not one-one

Step 1: For every integer (n), taking (x=n) gives (\lfloor x\rfloor=n), so it is onto (\mathbb{Z}). Step 2: But (\lfloor 2.1\rfloor=\lfloor 2.9\rfloor=2), so it is not one-one. Step 3: Changing the codomain to (\mathbb{Z}) makes this function onto.