Algebra Questions

Question Number 147942 by mathdanisur last updated on 24/Jul/21

$${if}\:\:\:{f}\left({x}\right)={f}\left({x}−\mathrm{4}\right)+\mathrm{8}\:\:\:{and}\:\:\:{f}\left(\mathrm{2}\right)=\mathrm{4} \\$$$${find}\:\:\:{f}\left(\mathrm{10}\right)=? \\$$

Answered by Olaf_Thorendsen last updated on 24/Jul/21

$${f}\left({x}\right)\:=\:{f}\left({x}−\mathrm{4}\right)+\mathrm{8} \\$$$$\\$$$$\bullet\:{f}\left(\mathrm{6}\right)\:=\:{f}\left(\mathrm{6}−\mathrm{4}\right)+\mathrm{8}\:=\:{f}\left(\mathrm{2}\right)+\mathrm{8}\:=\:\mathrm{12} \\$$$$\\$$$$\bullet\:{f}\left(\mathrm{10}\right)\:=\:{f}\left(\mathrm{10}−\mathrm{4}\right)+\mathrm{8}\:=\:{f}\left(\mathrm{6}\right)+\mathrm{8}\:=\:\mathrm{20} \\$$$$\\$$$${f}\left(\mathrm{10}\right)\:=\:\mathrm{20} \\$$

Commented by mathdanisur last updated on 24/Jul/21

$${Thank}\:{you}\:{Ser} \\$$

Answered by Rasheed.Sindhi last updated on 25/Jul/21

$${f}\left({x}\right)={f}\left({x}−\mathrm{4}\right)+\mathrm{8}\:;\:{f}\left(\mathrm{2}\right)=\mathrm{4}\:;\:{f}\left(\mathrm{10}\right)=? \\$$$$\:{x}={x}−\mathrm{4}:\:\: \\$$$$\:\:\:\:\:\:{f}\left({x}−\mathrm{4}\right)={f}\left({x}−\mathrm{8}\right)+\mathrm{8} \\$$$${f}\left({x}\right)=\left({f}\left({x}−\mathrm{8}\right)+\mathrm{8}\right)+\mathrm{8}={f}\left({x}−\mathrm{8}\right)+\mathrm{16} \\$$$$\:\:\:{f}\left(\mathrm{10}\right)={f}\left(\mathrm{10}−\mathrm{8}\right)+\mathrm{16} \\$$$$\:\:\:\:\:\:\:\:\:\:\:\:\:={f}\left(\mathrm{2}\right)+\mathrm{16}=\mathrm{4}+\mathrm{16}=\mathrm{20} \\$$

Commented by mathdanisur last updated on 25/Jul/21

$${Thank}\:{you}\:{Ser} \\$$