Question Number 192648 by pascal889 last updated on 24/May/23
$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)\right) \\ $$$$\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\boldsymbol{\mathrm{x}}^{\mathrm{3}} −\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{3}\boldsymbol{\mathrm{x}} \\ $$$$\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{x}}\right)=\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{1} \\ $$
Answered by Skabetix last updated on 24/May/23
$${g}\left({f}\left({x}\right)\right)=\left({x}^{\mathrm{3}} −{x}^{\mathrm{2}} +\mathrm{3}{x}\right)^{\mathrm{2}} −\mathrm{2}\left({x}^{\mathrm{3}} −{x}^{\mathrm{2}} +\mathrm{3}{x}\right)+\mathrm{1}={x}^{\mathrm{6}} −\mathrm{2}{x}^{\mathrm{5}} +\mathrm{7}{x}^{\mathrm{4}} −\mathrm{8}{x}^{\mathrm{3}} +\mathrm{11}{x}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{1} \\ $$