Answer
$f \,\,is\,\,not\,one-to-one$
Work Step by Step
$A\,function\,\,F: X \rightarrow Y\,is\,not\,\,\,one-to-one\,\Leftrightarrow \\
\exists \,\,x_{1}\,and\,x_{2}\,\,in\,\,X\,\,such\,that\,\,
F(x_{1}) = F(x_{2})\,\,and x_{1} \neq x_{2}.\\
f:\mathbb{R}\rightarrow \mathbb{R},f(x)=\frac{x}{x^2+1}\\
f(3)=f(\frac{1}{3})=\frac{3}{10}\,\,and\,\,3\neq \frac{1}{3}
\\
f \,\,is\,\,not\,one-to-one$
