Let \( f: R \rightarrow R \) be defined as \( f(x)=2 x-1 \) and \( g: R-\{1\} \rightarrow R-\{1\} \) be defined a \( g(x…

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

[JEE Main 2021, 24 Feb (Shift 1)]