Category: Relation and Functions

Question Number 93331 by john santu last updated on 12/May/20 $$\mathrm{If}\mathrm{f}(\mathrm{x}+\mathrm{y})=\mathrm{f}\left(\mathrm{x}\right)+\mathrm{f}\left(\mathrm{y}\right)\mathrm{and}$$$$\mathrm{f}\left(1\right)=5\mathrm{then}\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{value}$$$$\mathrm{of}\mathrm{f}\left(2020\right)?$$ Commented by mr W last updated on 12/May/20…

Question Number 158862 by mathlove last updated on 09/Nov/21 Answered by gsk2684 last updated on 09/Nov/21 $$f\left(x\right)+2f\left(\frac{1}{x}\right)=x\dots \left(1\right)$$$$replacexby\frac{1}{x}$$$$f\left(\frac{1}{x}\right)+2f\left(x\right)=\frac{1}{x}\Rightarrow \frac{x-f\left(x\right)}{2}+2f\left(x\right)=\frac{1}{x}$$$$\frac{x-f\left(x\right)+4f\left(x\right)}{2}=\frac{1}{x}\Rightarrow x+3f\left(x\right)=\frac{2}{x}$$$$\mathrm{3}{f}\left({x}\right)=\frac{\mathrm{2}}{{x}}−{x}\Rightarrow{f}\left({x}\right)=\frac{\mathrm{2}−{x}^{\mathrm{2}}…

Question Number 27784 by abdo imad last updated on 14/Jan/18 $$letgivef\left(x\right)=e^{-\frac{1}{x}}withf\left(0\right)=0$$$$1)isfderivableinpoint0?$$$$2)provethat{f}^{\left(n\right)}=F_n\left(x\right)e^{-\frac{1}{x}}with{F}_{n}isrationalfunction$$$$\left.\mathrm{3}\right)\:{calculate}\:\:\:{f}^{\left(\mathrm{6}\right)} \:\left({x}\right)\:{and}\:\:{f}^{\left(\mathrm{9}\right)} \left({x}\right)\:\:. \…

Question Number 27618 by NECx last updated on 11/Jan/18 $$Findtherangeofy=x(x^6-1).For$$$$whichy=0$$ Answered by mrW2 last updated on 13/Jan/18 $${y}={x}\left({x}^{\mathrm{6}} −\mathrm{1}\right)=\mathrm{0} \…

Question Number 92933 by mathmax by abdo last updated on 09/May/20 $$provethstforz\in C-Z{\left(\frac{\pi z}{sin\left(\pi z\right)}\right)}^2=\sum _{n=-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{1}{{(z-n)}^2}$$$${and}\:\:\frac{\left(\pi{z}\right)^{\mathrm{2}} }{{sin}^{\mathrm{2}} \left(\pi{z}\right)}{cos}\left(\pi{z}\right)\:=\sum_{{n}=−\infty} ^{+\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{\left({z}−{n}\right)^{\mathrm{2}} } \…