In this paper, with the help of the properties of the classes of additive functions, $\mathbb{Q}$-homogeneous and quadratic, we try to obtain the solutions of the Pexider functional equation
for the pairs $(x,y)\in \mathbb{R}^2$, by the condition of functional equation for the equation and considering a constrained polynomial of two variables $P(x,y)=0$. By choosing linear or power criteria for the constrained polynomial, we present the properties of the functions $f_1$ and $f_2$ in the Pexider functional equation. We will also prove similar results in functional equations involving the classes of additive, quadratic, and derivation functions.
