Category: Relation and Functions

Question Number 19982 by Tinkutara last updated on 19/Aug/17 $$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{ordered}\mathrm{pairs}$$$$(A,B)\mathrm{where}A\mathrm{and}B\mathrm{are}\mathrm{subsets}\mathrm{of}$$$$\{1,2,\dots ,5\}\mathrm{such}\mathrm{that}\mathrm{neither}A\subseteq B$$$$\mathrm{nor}B\subseteq A?$$ Commented by mrW1 last updated on 22/Aug/17…

Question Number 85500 by oustmuchiya@gmail.com last updated on 22/Mar/20 $$Thefunctionof\mathbf{f}and\mathbf{g}aredefinedby\mathbf{f}:\mathbf{g}\to \frac{x}{\mathbf{b}x-2},x\ne \frac{2}{\mathbf{b}}and\mathbf{b}\ne 0,where\mathbf{a}and\mathbf{b}arerealnumbers\mathbf{g}:\mathbf{x}\to 2x-11$$$$\left(a\right)If\mathbf{f}\left(2\right)=\frac{-1}{2}and{\mathbf{f}}^{-1}\left(1\right)=-1,find\mathbf{a}and\mathbf{b}andwritedowntheexpressionfor\mathbf{f}intermsof\mathbf{x}$$$$\left(\mathbf{b}\right)\mathbf{F}indthevalueof\mathbf{x}forwhich\mathbf{fg}\left(\mathbf{x}\right)=\frac{-1}{2}$$ Answered by john santu last updated on 22/Mar/20…

Question Number 85425 by john santu last updated on 22/Mar/20 $$rangeoffunction$$$$y=\frac{\mid x-1\mid }{x+3}$$ Answered by john santu last updated on 22/Mar/20 $${for}\:{x}\:\geqslant\mathrm{1}\:\Rightarrow\:{y}\:=\:\frac{{x}−\mathrm{1}}{{x}+\mathrm{3}} \…

Question Number 85233 by jagoll last updated on 20/Mar/20 $$\mathrm{what}\mathrm{is}\mathrm{domain}\mathrm{of}\mathrm{x}\mathrm{for}$$$$\mathrm{f}\left(\mathrm{x}\right)+2\mathrm{f}(1-\mathrm{x})={\mathrm{x}}^2$$ Commented by jagoll last updated on 20/Mar/20 $$\mathrm{replace}1-\mathrm{x}\mathrm{by}\mathrm{x}$$$$\mathrm{f}\left(\mathrm{1}−\mathrm{x}\right)+\mathrm{2f}\left(\mathrm{x}\right)\:=\:\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{2}} \:\left(\mathrm{ii}\right)…

Question Number 85164 by mathmax by abdo last updated on 19/Mar/20 $$calculate\sum _{n=0}^{\mathrm{\infty }}arctan\left(\frac{1}{n^2+n+1}\right)$$ Commented by Cmr 237 last updated on 19/Mar/20…