Question Number 204610 by mnjuly1970 last updated on 23/Feb/24
$$ \\ $$$$\:\:\:{If}\:,\:\:\:{f}\left({x}\right)\:=\:\begin{cases}{\:\mathrm{2}^{\mathrm{2}{x}} −\:{log}_{\mathrm{3}} \:\left(\:{x}+\mathrm{3}\:\right)\:\:\:\:;\:\:\:{x}\:\geqslant\mathrm{5}}\\{\:{f}\:\left(\mathrm{1}+\:{x}\:\right)\:\:−\mathrm{4}\:\:\:\:\:\:\:\:\:\:\:\:\:\:;\:\:{x}\:<\:\mathrm{5}}\end{cases}\:\:\:\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\Rightarrow\:\:{f}\:\left(\mathrm{0}\:\right)=\:? \\ $$$$ \\ $$
Answered by Rasheed.Sindhi last updated on 23/Feb/24
$${f}\left(\mathrm{0}\right)={f}\left(\mathrm{1}\right)−\mathrm{4} \\ $$$$\:\:\:\:\:\:\:\:\:\:={f}\left(\mathrm{2}\right)−\mathrm{8} \\ $$$$\:\:\:\:\:\:\:\:\:\:={f}\left(\mathrm{3}\right)−\mathrm{12} \\ $$$$\:\:\:\:\:\:\:\:\:={f}\left(\mathrm{4}\right)−\mathrm{16} \\ $$$$\:\:\:\:\:\:\:\:\:={f}\left(\mathrm{5}\right)−\mathrm{20} \\ $$$$\:\:\:\:\:\:\:\:\:=\mathrm{2}^{\mathrm{2}\left(\mathrm{5}\right)} −\mathrm{log}_{\mathrm{3}} \left(\mathrm{5}+\mathrm{3}\right)−\mathrm{20} \\ $$$$\:\:\:\:\:\:\:\:=\mathrm{1004}−\mathrm{log}_{\mathrm{3}} \left(\mathrm{8}\right)\: \\ $$