Let \(g : R \rightarrow R\) be a non constant twice differentiable function such that \(g ^{\prime}\left(\frac{1}{2}\rig…

Let \(g : R \rightarrow R\) be a non constant twice differentiable function such that \(g ^{\prime}\left(\frac{1}{2}\right)= g ^{\prime}\left(\frac{3}{2}\right)\). If a real valued function \(f\) is defined as \(f(x)=\frac{1}{2}[g(x)+g(2-x)]\), then

[JEE Main 2024, 30 Jan (Shift 1)]