Answer
f is one-to-one
Work Step by Step
$f(x)=\frac{3x-1}{x}\\
A\,function\,\,f: \mathbb{R}^\ast \rightarrow \mathbb{R}^\ast \,is\,\,one-to-one\,\Leftrightarrow \\
\forall \,\,x_{1}\,and\,x_{2}\,\,in\,\,\mathbb{R}^\ast \,\,if\,
f(x_{1}) = f(x_{2})\,\,then\,x_{1} = x_{2}.\\
let\,f(x_{1})=f(x_{2})\\
\Rightarrow \frac{3x_{1}-1}{x_{1}}=\frac{3x_{2}-1}{x_{2}}\\
\Rightarrow (3x_{1}-1)x_{2}=(3x_{2}-1)x_{1}\\
\Rightarrow 3x_{2}x_{1}-x_{2}=3x_{2}x_{1}-x_{1}\\
\Rightarrow -x_{1}=-x_{2}\\
\Rightarrow x_{1}=x_{2}\\
therefore\,f\,is\,one-to-one
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