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Question-210971




Question Number 210971 by black_mamba234 last updated on 25/Aug/24
Answered by A5T last updated on 25/Aug/24
2) 2x_1 +4y_1 −2z_1 =2(x_1 +k)+4y_1 −2(z_1 +k)  f(x_1 ,y_1 ,z_1 )=f(x_2 ,y_2 ,z_2 )⇏(x_1 ,y_1 ,z_1 )=(x_2 ,y_2 ,z_2 )  ⇒ f is not injective.
$$\left.\mathrm{2}\right)\:\mathrm{2}{x}_{\mathrm{1}} +\mathrm{4}{y}_{\mathrm{1}} −\mathrm{2}{z}_{\mathrm{1}} =\mathrm{2}\left({x}_{\mathrm{1}} +{k}\right)+\mathrm{4}{y}_{\mathrm{1}} −\mathrm{2}\left({z}_{\mathrm{1}} +{k}\right) \\ $$$${f}\left({x}_{\mathrm{1}} ,{y}_{\mathrm{1}} ,{z}_{\mathrm{1}} \right)={f}\left({x}_{\mathrm{2}} ,{y}_{\mathrm{2}} ,{z}_{\mathrm{2}} \right)\nRightarrow\left({x}_{\mathrm{1}} ,{y}_{\mathrm{1}} ,{z}_{\mathrm{1}} \right)=\left({x}_{\mathrm{2}} ,{y}_{\mathrm{2}} ,{z}_{\mathrm{2}} \right) \\ $$$$\Rightarrow\:{f}\:{is}\:{not}\:{injective}. \\ $$

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