Question Number 1307 by Rasheed Ahmad last updated on 21/Jul/15 $${f}\left(\mathrm{2}{x}\right)−\mathrm{2}\left[\:{f}\left({x}\right)\:\right]^{\mathrm{2}} +\mathrm{1}=\mathrm{0} \\ $$$${f}\left({x}\right)=? \\ $$ Commented by Rasheed Soomro last updated on 22/Jul/15 $$\left({Rasheed}\:{Ahmad}\right)…
Question Number 1302 by Rasheed Ahmad last updated on 20/Jul/15 $${Generalization}\:{of}\:{Q}\:{No}\:\mathrm{1296} \\ $$$${f}\left({x}+{k}\right)=\left[\:{f}\left({x}\right)\:\right]^{{n}} \\ $$$${f}\left({x}\right)=? \\ $$ Answered by prakash jain last updated on 21/Jul/15…
Question Number 66833 by ~ À ® @ 237 ~ last updated on 20/Aug/19 $${Somewhere}\:,\:{there}\:{are}\:{scorpio},\:{snake}\:{and}\:{mouse}. \\ $$$${We}\:{ascertain}\:{that}\:: \\ $$$${Every}\:{morning}\:,\:{each}\:{snake}\:{eats}\:{a}\:{mouse}\:. \\ $$$${Every}\:{afternoon}\:,{each}\:{scorpio}\:\:{kills}\:{a}\:{snake}. \\ $$$${And}\:{every}\:{night}\:,\:{each}\:{mouse}\:{eats}\:{a}\:{scorpio}. \\ $$$${Two}\:{weeks}\:{passed}\:{and}\:{we}\:{find}\:{that}\:{there}\:{was}\:{remaining}\:{only}\:{one}\:{animal}\:.…
Question Number 66827 by mr W last updated on 20/Aug/19 Commented by mr W last updated on 20/Aug/19 $${the}\:{graph}\:{above}\:{shows}\:{the}\:{equation} \\ $$$$\frac{\mathrm{ln}\:\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}=\frac{\mathrm{ln}\:\left({y}+\sqrt{\mathrm{1}+{y}^{\mathrm{2}} }\right)}{\:\sqrt{\mathrm{1}+{y}^{\mathrm{2}} }}…
Question Number 1289 by Rasheed Soomro last updated on 19/Jul/15 $${Prove}\:{that}\: \\ $$$$\:\:''\:{f}\left(\:{f}\left({x}\right)\:\right)\:{is}\:{polynomial}\:''\:\Rightarrow\:''\:{f}\left({x}\right)\:{is}\:{rational}\:{expression}\:'' \\ $$$$\:{Or}\:{give}\:{a}\:{counter}\:{example}\:. \\ $$$$ \\ $$ Answered by prakash jain last updated…
Question Number 132358 by Engr_Jidda last updated on 13/Feb/21 $${find}\:{the}\:{equation}\:{whose}\:{roots}\:{are} \\ $$$$\alpha\:{and}\:\beta.\:{find}\:\alpha\:{and}\:\beta\:{if}\:\:\alpha−\beta=\mathrm{2}\:{and}\:\alpha^{\mathrm{2}} −\beta^{\mathrm{2}} =\mathrm{3} \\ $$ Commented by Dwaipayan Shikari last updated on 13/Feb/21 $${x}^{\mathrm{2}}…
Question Number 1280 by Rasheed Soomro last updated on 19/Jul/15 $$\:{f}\:\left(\:\frac{\mathrm{1}}{{f}\left({x}\right)}\right)={f}\left({x}\right)\: \\ $$$${f}\left({x}\right)=? \\ $$ Commented by 123456 last updated on 19/Jul/15 $${f}\left({x}\right)=\frac{\mathrm{1}}{{x}} \\ $$…
Question Number 1278 by Rasheed Soomro last updated on 19/Jul/15 $${Determine}\:{f}\left({x}\right)\:{when}\:{f}\left(\:{f}\left({x}\right)\right)={x}\:\:. \\ $$ Commented by prakash jain last updated on 19/Jul/15 $${f}\left({x}\right)=\frac{{ax}+{b}}{{cx}+{d}} \\ $$$${f}\left({f}\left({x}\right)\right)=\frac{{a}\frac{{ax}+{b}}{{cx}+{d}}+{b}}{{c}\frac{{ax}+{b}}{{cx}+{d}}+{d}}={x} \\…
Question Number 1260 by Rasheed Ahmad last updated on 18/Jul/15 $$\mathrm{What}\:\mathrm{is}\:\mathrm{degree}\:\mathrm{of}\:\frac{\mathrm{x}}{\mathrm{y}}\:?\:\left(\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{are}\:\mathrm{both}\:\mathrm{variables}\right) \\ $$$$\mathrm{Is}\:\frac{\mathrm{x}}{\mathrm{y}}\:\:\mathrm{and}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{of}\:\mathrm{same}\:\mathrm{degree}? \\ $$ Commented by prakash jain last updated on 18/Jul/15 $$\mathrm{Degree}\:\mathrm{of}\:\mathrm{rational}\:\mathrm{expression}\:\mathrm{is}\:\mathrm{the}\:\mathrm{degree} \\…
Question Number 1239 by Rasheed Ahmad last updated on 17/Jul/15 $${Rasheed}\:{Ahmad}\:\left({Rasheed}\:{Soomro}\right) \\ $$$$\bullet\mathrm{For}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{where}\:\mathrm{x}\:\mathrm{and}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{both}\:{are} \\ $$$$\mathrm{real}\:\mathrm{the}\:\left(\mathrm{x},{f}\left({x}\right)\right)\:{can}\:{be}\:{plotted}\:{as} \\ $$$${a}\:{point}\:{easily}.\:\bullet{Now}\:{consider}\:{F}\left({X}\right) \\ $$$${where}\:{X}\:{and}\:{F}\left({X}\right)\:{are}\:{complex}\: \\ $$$${numbers}.\:{How}\:{can}\:\left({X},{F}\left({X}\right)\right)\:{be} \\ $$$${plotted}?\:{For}\:{a}\:{particular}\:{example}:\:\left(\mathrm{3}+\mathrm{2}{i},\mathrm{4}−\mathrm{5}{i}\right) \\ $$$${how}\:{can}\:{be}\:{plotted}?…