Let R\mathbf{R}R denote the set of all real numbers. Find all functions f:R→Rf: \mathbf{R} \to \mathbf{R}f:R→R such that
f(x2+f(y))=y+(f(x))2for all x,y∈R.f \left(x^2 + f(y)\right) = y + \left(f(x)\right)^2 \quad \text{for all } x, y \in R.f(x2+f(y))=y+(f(x))2for all x,y∈R.