Question Number 39650 by KMA last updated on 09/Jul/18
$${If}\:{f}\:{be}\:{a}\:{linear}\:{function}\:{f}\:\left(\mathrm{6}\right)−{f}\left(\mathrm{12}\right) \\ $$$$=\mathrm{2}\:{What}\:{is}\:{f}\left(\mathrm{12}\right)−{f}\left(\mathrm{2}\right). \\ $$$$ \\ $$
Answered by MrW3 last updated on 09/Jul/18
$${assume}\:{f}\left({x}\right)={ax}+{b} \\ $$$${f}\left(\mathrm{6}\right)−{f}\left(\mathrm{12}\right)=\mathrm{6}{a}+{b}−\left(\mathrm{12}{a}+{b}\right)=−\mathrm{6}{a}=\mathrm{2} \\ $$$$\Rightarrow{a}=−\frac{\mathrm{1}}{\mathrm{3}} \\ $$$${f}\left(\mathrm{12}\right)−{f}\left(\mathrm{2}\right)=\mathrm{12}{a}+{b}−\left(\mathrm{2}{a}+{b}\right)=\mathrm{10}{a}=−\frac{\mathrm{10}}{\mathrm{3}} \\ $$