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