Question Number 166402 by mathls last updated on 19/Feb/22
$${f}\left({x}\right)={x}^{\mathrm{3}} +{x}^{\mathrm{2}} +\mathrm{13} \\ $$$${g}\left({x}\right)=\sqrt{\mathrm{5}} \\ $$$${gof}_{\left({x}\right)} =? \\ $$
Answered by alephzero last updated on 19/Feb/22
$$\left({g}\:\circ\:{f}\right)\left({x}\right)\:\equiv\:{g}\left({f}\left({x}\right)\right) \\ $$$$\mathrm{If}\:{g}\left({x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{constant}\:\Rightarrow \\ $$$$\Rightarrow\:\left({g}\:\circ\:{f}\right)\left({x}\right)\:=\:{g}\left({f}\left({x}\right)\right)\:=\:{g}\left({x}\right) \\ $$$$\left({g}\:\circ\:{f}\right)\left({x}\right)\:=\:{g}\left({f}\left({x}\right)\right)\:=\:{g}\left({x}\right)\:=\:\sqrt{\mathrm{5}} \\ $$