Let f: R → R be defined as f(x)=2 x-1 and g: R -{1} → R be defined as g(x)=(x-1/2)/(x-1). Then the composition function f(g(x)) is:

Let $\displaystyle f: \mathbf{R} \rightarrow \mathbf{R}$ be defined as $\displaystyle f(x)=2 x-1$ and $\displaystyle g: \mathbf{R}-\{1\} \rightarrow \mathbf{R}$ be defined as $\displaystyle g(x)=\frac{x-\dfrac{1}{2}}{x-1}$. Then the composition function $\displaystyle f(g(x))$ is :