Question Number 75083 by Rio Michael last updated on 07/Dec/19
$${A}\:{function}\:{f}\:{is}\:{given}\:{by}\: \\ $$$$\:{f}\left({x}\right)\:=\:\begin{cases}{{x}^{\mathrm{2}} −\mathrm{3},\:\:\mathrm{0}\leqslant{x}<\mathrm{2}}\\{\mathrm{4}{x}−\mathrm{7},\:\mathrm{2}\leqslant{x}<\mathrm{4}}\end{cases} \\ $$$${is}\:{such}\:{that}\:{f}\left({x}\right)\:=\:{f}\left({x}\:+\:\mathrm{4}\right)\: \\ $$$${find}\:\:{f}\left(\mathrm{27}\right)\:{and}\:{f}\left(−\mathrm{106}\right). \\ $$
Answered by MJS last updated on 07/Dec/19
$$\mathrm{27}=\mathrm{6}×\mathrm{4}+\mathrm{3} \\ $$$$−\mathrm{106}=−\mathrm{27}×\mathrm{4}+\mathrm{2} \\ $$$$\Rightarrow \\ $$$${f}\left(\mathrm{27}\right)={f}\left(\mathrm{3}\right)=\mathrm{5} \\ $$$${f}\left(−\mathrm{106}\right)={f}\left(\mathrm{2}\right)=\mathrm{1} \\ $$
Commented by Rio Michael last updated on 07/Dec/19
$${thank}\:{you}\:{sir},\:{i}\:{got}\:{the}\:{now} \\ $$