Category: Algebra

Question Number 1280 by Rasheed Soomro last updated on 19/Jul/15 $$f\left(\frac{1}{f\left(x\right)}\right)=f\left(x\right)$$$$f\left(x\right)=?$$ Commented by 123456 last updated on 19/Jul/15 $$f\left(x\right)=\frac{1}{x}$$…

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 66769 by John Kaloki Musau last updated on 19/Aug/19 $$simplify$$$$\frac{x+4}{x-4}-\frac{5x+20}{x^2-16}$$ Commented by Prithwish sen last updated on 19/Aug/19…

Question Number 1229 by Rasheed Soomro last updated on 16/Jul/15 $$f\left(f\left(x\right)\right)=x^2-x+1$$$$f\left(x\right)=?$$$$\left(ModificationofQ1147\right)$$ Commented by 123456 last updated on 17/Jul/15…

Question Number 132295 by shaker last updated on 13/Feb/21 Commented by mathmax by abdo last updated on 13/Feb/21 $$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{logx}-\sqrt{5\mathrm{x}-5}\mathrm{f}\mathrm{defined}\mathrm{on}[1,+\mathrm{\infty }[$$$${\mathrm{f}}^{{}^{\prime }}\left(\mathrm{x}\right)=\frac{1}{\mathrm{x}}-\frac{5}{2\sqrt{5\mathrm{x}-5}}=\frac{1}{\mathrm{x}}-\frac{\sqrt{5}}{2\sqrt{\mathrm{x}-1}}=\frac{2\sqrt{\mathrm{x}-1}-\sqrt{5}\mathrm{x}}{2\mathrm{x}\sqrt{\mathrm{x}-1}}$$$$=\frac{\left(\mathrm{2}\sqrt{\mathrm{x}−\mathrm{1}}−\sqrt{\mathrm{5}}\mathrm{x}\right)\left(\mathrm{2}\sqrt{\mathrm{x}−\mathrm{1}}+\sqrt{\mathrm{5}}\mathrm{x}\right)}{\mathrm{2x}\sqrt{\mathrm{x}−\mathrm{1}}\left(\mathrm{2}\sqrt{\mathrm{x}−\mathrm{1}}+\sqrt{\mathrm{5}}\mathrm{x}\right)}\:=\frac{\mathrm{4}\left(\mathrm{x}−\mathrm{1}\right)−\mathrm{5x}^{\mathrm{2}} }{\left(…\right)}=\frac{−\mathrm{5x}^{\mathrm{2}}…