Question Number 48741 by peter frank last updated on 28/Nov/18
Answered by tanmay.chaudhury50@gmail.com last updated on 28/Nov/18
$${g}\left({x}\right)=\frac{{x}^{\mathrm{2}} −\mathrm{16}}{{x}−\mathrm{4}}\:{x}\neq\mathrm{4} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:={x}+\mathrm{4} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:={t}\:\:\:\:{x}=−\mathrm{4}\:\left({that}\:{is}\:{x}+\mathrm{4}=\mathrm{0}\right) \\ $$$${now}\:{to}\:{find}\:{t}\:{such}\:{that}\:{f}\left({x}\right)={g}\left({x}\right)\:\:{for}\:{all}\: \\ $$$${values}\:{of}\:{x} \\ $$$${but}\:{x}\neq\mathrm{4}\:\:{for}\:{g}\left({x}\right) \\ $$$${so}\:{f}\left({x}\right)\neq{g}\left({x}\right)\:{at}\:{x}=\mathrm{4} \\ $$$${at}\:{x}=\mathrm{4}\:\:\:{f}\left({x}\right)=\mathrm{4}−\mathrm{4}=\mathrm{0} \\ $$$${but}\:{g}\left({x}\right)\:{is}\:{undefined}\:{at}\:{x}=\mathrm{4} \\ $$$${however}\:{at}\:{x}=−\mathrm{4}\:{f}\left({x}\right)\:=−\mathrm{4}−\mathrm{4}=−\mathrm{8} \\ $$$${so}\:{t}\:{should}\:{be}\:{x}−\mathrm{4}\: \\ $$$${pls}\:{check}\:{the}\:{question}... \\ $$$$ \\ $$
Commented by peter frank last updated on 28/Nov/18
$$\mathrm{your}\:\mathrm{right}\:\mathrm{sir} \\ $$