Category: Relation and Functions

Question Number 76657 by Tony Lin last updated on 29/Dec/19 $$provethat{sin}^{-1}\left(tanhx\right)={tan}^{-1}\left(sinhx\right)$$ Answered by john santu last updated on 29/Dec/19 $$\left(\mathrm{1}\right)\:\mathrm{tan}\:{hx}\:=\:\mathrm{sin}\:{y} \…

Question Number 11067 by suci last updated on 10/Mar/17 $$ifE=\{f\mid f:\mathbb{R}\to \mathbb{R}continuousfunctionwithf\left(x\right)\in \mathbb{Q},\mathrm{\forall }x\in \mathbb{R}\},$$$$thenE=\dots .???$$ Commented by FilupS last updated on 10/Mar/17 $$\mathbb{Q}=\mathrm{irrational}\mathrm{numbers}\mathrm{set}$$$$ \…

Question Number 10987 by Joel576 last updated on 05/Mar/17 $$\mathrm{If}$$$$\bullet f(2x+1)+g(3-x)=x$$$$\bullet f\left(\frac{3x+5}{x+1}\right)+2g\left(\frac{2x+1}{x+1}\right)=\frac{x}{x+1}$$$$\mathrm{for}\mathrm{every}x\in \mathbb{R},x\ne -1$$$$\mathrm{Find}f\left(x\right)!!$$ Answered by ajfour last updated…

Question Number 76497 by mathmax by abdo last updated on 27/Dec/19 $$calculatetan\left(3x\right)intermsoftanx$$ Answered by Rio Michael last updated on 27/Dec/19 $$tan3x=tan(2x+x)=\frac{tan2x+tanx}{1-tan2xtanx}$$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\frac{\frac{\mathrm{2}{tanx}}{\mathrm{1}−{tan}^{\mathrm{2}}…

Question Number 10887 by Saham last updated on 28/Feb/17 $$\mathrm{Suppose}\mathrm{that}\mathrm{f}\left(\mathrm{x}\right)=\frac{1}{\mathrm{x}+1}\mathrm{and}\mathrm{g}\left(\mathrm{x}\right)=\frac{4}{\mathrm{x}+1}.$$$$\mathrm{Find}\mathrm{the}\mathrm{domain}\mathrm{of}\mathrm{each}\mathrm{of}\mathrm{the}\mathrm{composition}$$$$\left(\mathrm{a}\right)\mathrm{f}\mathrm{o}\mathrm{g}\left(\mathrm{b}\right)\mathrm{f}\mathrm{o}\mathrm{f}$$ Answered by geovane10math last updated on 28/Feb/17 $$\mathrm{I}\:\mathrm{wrote}\:\mathrm{an}\:\mathrm{answer} \…