Question Number 187612 by SEKRET last updated on 19/Feb/23
$$\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}\right)\right)+\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{y}}\right)=\mathrm{2}\boldsymbol{\mathrm{y}}+\boldsymbol{\mathrm{f}}^{\mathrm{2}} \left(\boldsymbol{\mathrm{x}}\right) \\ $$$$\:\boldsymbol{\mathrm{f}}\::\boldsymbol{\mathrm{R}}\rightarrow\boldsymbol{\mathrm{R}} \\ $$