Let \(f: \mathbf{R}-\left\{\frac{-1}{2}\right\} \rightarrow \mathbf{R}\) and \(g: \mathbf{R}-\left\{\frac{-5}{2}\right\}…

Let \(f: \mathbf{R}-\left\{\frac{-1}{2}\right\} \rightarrow \mathbf{R}\) and \(g: \mathbf{R}-\left\{\frac{-5}{2}\right\} \rightarrow \mathbf{R}\) be defined as \(f(x)=\frac{2 x+3}{2 x+1}\) and \(g(x)=\frac{|x|+1}{2 x+5}\). Then, the domain of the function \(fog\) is :

[JEE Main 2024, 27 Jan (Shift 2)]