Category: Relation and Functions

Question Number 193685 by cortano12 last updated on 18/Jun/23 $${\left(\mathrm{f}\left(\mathrm{x}\right)\right)}^2-4\mathrm{xf}\left(\mathrm{x}\right)+3=0$$$${\mathrm{f}}^{-1}\left(3\right)=?$$ Answered by mr W last updated on 18/Jun/23 $${y}^{\mathrm{2}}…

Question Number 193267 by Mingma last updated on 09/Jun/23 Answered by cortano12 last updated on 09/Jun/23 $$\left(\mathrm{i}\right)4\mathrm{f}\left(\mathrm{x}\right)+\mathrm{f}\left(\frac{1}{\mathrm{x}}\right)=24\mathrm{x}+5+\frac{6}{\mathrm{x}}$$$$\left(\mathrm{ii}\right)4\mathrm{f}\left(\frac{1}{\mathrm{x}}\right)+\mathrm{f}\left(\mathrm{x}\right)=\frac{24}{\mathrm{x}}+5+6\mathrm{x}$$$$\left(\mathrm{i}\right)\times 4=4\mathrm{f}\left(\frac{1}{\mathrm{x}}\right)+16\mathrm{f}\left(\mathrm{x}\right)=96\mathrm{x}+20+\frac{24}{\mathrm{x}}$$$$\left(\mathrm{i}\right)-\left(\mathrm{ii}\right)$$$$\:\:\:\Rightarrow\mathrm{15f}\left(\mathrm{x}\right)=\mathrm{90x}+\mathrm{15}…

Question Number 65488 by mathmax by abdo last updated on 30/Jul/19 $$U_{n}isasequencewichverify\mathrm{\forall }n\in N^{★}$$$$U_n+U_{n+1}=\frac{1}{n}$$$$1)calculate{U}_{n}intermsofn$$$$2)isthesequence{U}_{n}convergent?$$…

Question Number 65402 by mathmax by abdo last updated on 29/Jul/19 $$solvethe\left(de\right)\sqrt{x^2+1}{y}^{{}^{″}}-{xy}^{{}^{\prime }}=x^2-x$$ Commented by mathmax by abdo last updated…

Question Number 65386 by mathmax by abdo last updated on 29/Jul/19 $$calculate\sum _{k=1}^{\mathrm{\infty }}\frac{{(-1)}^{k-1}}{99k-1}$$ Commented by mathmax by abdo last updated on…