Answer
$f(x)=\left \lfloor x \right \rfloor f:\mathbb{R}\rightarrow \mathbb{Z} \\$
$f\,\,is\,onto\,$
$f\,\,is\,not\,one-to-one$
Work Step by Step
$f(x)=\left \lfloor x \right \rfloor f:\mathbb{R}\rightarrow \mathbb{Z} \\
f: \mathbb{R} \rightarrow \mathbb{Z}\,\,is\,\,onto\,\Leftrightarrow \,\\
\forall y\,in\,\mathbb{Z} ,\exists x \in \mathbb{R}\,such\,that\, f(x) = y.\\
and\,this\,true\,from\,the\,def.\,of\,floor\,function\,.\\
Floor Function:\,the\,greatest\,integer\,that\,is\,less\,than\,or\,equal\,to\,x \\
but\,f(x)=\,\left \lfloor x \right \rfloor \,is\,\,not\,one-to-one \\
A\,function\,\,F: \mathbb{R} \rightarrow \mathbb{Z}\,is\,not\,\,\,one-to-one\,\Leftrightarrow \\
\exists \,\,x_{1}\,and\,x_{2}\,\,in\,\,\mathbb{R}\,\,such\,that\,\,
F(x_{1}) = F(x_{2})\,\,and x_{1} \neq x_{2}.\\
we\,can\,see\,that\,\left \lfloor 2.1 \right \rfloor=\left \lfloor 2.2 \right \rfloor=2\\
and\,\,2.1\neq 2.2 \\
so\,f(x)=\,\left \lfloor x \right \rfloor \,is\,not\,one-to-one
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