Category: Relation and Functions

Question Number 158306 by mathlove last updated on 02/Nov/21 Commented by cortano last updated on 02/Nov/21 $$f(1-x)=\frac{4^{1-x}}{4^{1-x}+2}=\frac{\frac{4}{4^x}}{\frac{4}{4^x}+2}=\frac{4}{4+2.4^x}$$$${f}\left({x}\right)+{f}\left(\mathrm{1}−{x}\right)=\frac{\mathrm{4}^{{x}} }{\mathrm{4}^{{x}}…

Question Number 92767 by mathmax by abdo last updated on 09/May/20 $$let{U}_n={\int }_0^1{e}^{-nx}cosxdx$$$$1)determine{lim}_{n\to +\mathrm{\infty }}{n}^2{U}_n$$$$\left.\mathrm{2}\right){calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{U}_{{n}} \…

Question Number 92763 by msup by abdo last updated on 09/May/20 $$studythesequence{u}_{n+1}=\sqrt{u_n^2+\frac{1}{n}}$$$$and{u}_1=1$$ Commented by i jagooll last…

Question Number 158166 by cortano last updated on 31/Oct/21 $$Iff\left(\frac{x}{3}\right)=\frac{f\left(x\right)}{2}andf(1-x)=1-f\left(x\right).$$$$findf\left(\frac{173}{1993}\right).$$ Commented by SLVR last updated on 05/Nov/21 $$sircanyouprovidetheanswer$$ Terms…

Question Number 92597 by john santu last updated on 08/May/20 $$\mathrm{If}\mathrm{f}\left(\mathrm{x}\right)=\frac{1}{\mathrm{x}-1}\mathrm{and}\mathrm{g}\left(\mathrm{x}\right)=\sqrt{\mathrm{x}}$$$$\mathrm{find}\mathrm{domain}\mathrm{and}\mathrm{range}\mathrm{of}$$$$\mathrm{g}\left(\mathrm{f}\left(\mathrm{x}\right)\right).$$ Commented by jagoll last updated on 08/May/20 $$\mathrm{g}\left(\mathrm{f}\left(\mathrm{x}\right)\right)\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}−\mathrm{1}}}\:…