# Let $\; f:R\rightarrow R\;$ be defined as $f(x )=2x -1$ and $g:R-{1}\rightarrow R\;$ be defined as $g(x)=\frac{x-\frac{1}{2}}{x-1}$.Then the composition function $f\left ( g(x) \right )$ is: Option: 1 one-one but not onto Option: 2 neither one-one nor onto Option: 3 onto but not one-one Option: 4 both one-one and onto

\begin{aligned} &f(g(x))=2 g(x)-1\\ &=2 \frac{\left(x-\frac{1}{2}\right)}{x-1}=\frac{x}{x-1}\\ &f(g(x))=1+\frac{1}{x-1}\\ &\text { one-one, into } \end{aligned}

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