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Question-188560




Question Number 188560 by 073 last updated on 03/Mar/23
Answered by Rasheed.Sindhi last updated on 03/Mar/23
Let P(x)=ax+b  P(2x)=a(2x)+b=2ax+b  P(x)+P(2x)=6x+12  (ax+b)+(2ax+b)=6x+12  3ax+2b=6x+12  3a=6⇒a=2  2b=12⇒b=6  P(x)=ax+b=2x+6  P(3)=2(3)+6=12
$${Let}\:{P}\left({x}\right)={ax}+{b} \\ $$$${P}\left(\mathrm{2}{x}\right)={a}\left(\mathrm{2}{x}\right)+{b}=\mathrm{2}{ax}+{b} \\ $$$${P}\left({x}\right)+{P}\left(\mathrm{2}{x}\right)=\mathrm{6}{x}+\mathrm{12} \\ $$$$\left({ax}+{b}\right)+\left(\mathrm{2}{ax}+{b}\right)=\mathrm{6}{x}+\mathrm{12} \\ $$$$\mathrm{3}{ax}+\mathrm{2}{b}=\mathrm{6}{x}+\mathrm{12} \\ $$$$\mathrm{3}{a}=\mathrm{6}\Rightarrow{a}=\mathrm{2} \\ $$$$\mathrm{2}{b}=\mathrm{12}\Rightarrow{b}=\mathrm{6} \\ $$$${P}\left({x}\right)={ax}+{b}=\mathrm{2}{x}+\mathrm{6} \\ $$$${P}\left(\mathrm{3}\right)=\mathrm{2}\left(\mathrm{3}\right)+\mathrm{6}=\mathrm{12} \\ $$
Commented by 073 last updated on 03/Mar/23
thanks alot
$$\mathrm{thanks}\:\mathrm{alot} \\ $$
Answered by cortano12 last updated on 03/Mar/23
P(x)=2x+6⇒P(3)=12
$$\mathrm{P}\left(\mathrm{x}\right)=\mathrm{2x}+\mathrm{6}\Rightarrow\mathrm{P}\left(\mathrm{3}\right)=\mathrm{12} \\ $$
Commented by 073 last updated on 03/Mar/23
solution please
$$\mathrm{solution}\:\mathrm{please} \\ $$

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