Category: Relation and Functions

Question Number 84572 by msup trace by abdo last updated on 14/Mar/20 $$letF\left(z\right)=\frac{z^2}{1+z^7}$$$$1)factorizeinsideC\left[x\right]andR\left[x\right]$$$$z^7+1$$$$2)decomposeinsideC\left(x\right)andR\left(x\right)$$$${the}\:{fraction}\:{F}\left({x}\right) \…

Question Number 150044 by bramlexs22 last updated on 09/Aug/21 $$\mathrm{Given}\mathrm{f}\left(\frac{2\mathrm{x}-3}{2\mathrm{x}+1}\right)+\mathrm{f}\left(\frac{2\mathrm{x}+3}{1-2\mathrm{x}}\right)=4\mathrm{x}$$$$\mathrm{f}\left(\mathrm{x}\right)=?$$ Answered by liberty last updated on 09/Aug/21 $$\mathrm{f}\left(\frac{2\mathrm{x}-3}{2\mathrm{x}+1}\right)+\mathrm{f}\left(\frac{2\mathrm{x}+3}{1-2\mathrm{x}}\right)=4\mathrm{x}\dots \left(\mathrm{i}\right)$$$$\mathrm{let}\:\frac{\mathrm{2x}−\mathrm{3}}{\mathrm{2x}+\mathrm{1}}\:=\:\mathrm{y}\:; \…

Question Number 18859 by myintkhaing last updated on 31/Jul/17 $$\mathrm{If}\mathrm{f}(\mathrm{x}+2)=\mathrm{f}\left(\mathrm{x}\right)+7\mathrm{and}\mathrm{f}\left(1\right)=2;\mathrm{f}\left(2\right)=5,$$$$\mathrm{then}\mathrm{the}\mathrm{ratio}\mathrm{of}\mathrm{f}\left(150\right)\mathrm{to}\mathrm{f}\left(75\right)\mathrm{is}$$ Answered by 433 last updated on 31/Jul/17 $$$$$$ \…

Question Number 18575 by Tinkutara last updated on 25/Jul/17 $$\mathrm{If}\left(\right)\mathrm{represents}\mathrm{the}\mathrm{least}\mathrm{integer}\mathrm{function},$$$$\mathrm{then}\mathrm{the}\mathrm{value}\mathrm{of}\left(10\right)+(10+\frac{1}{20})+$$$$(10+\frac{2}{20})+\dots +(10+\frac{19}{20})\mathrm{is}\mathrm{equal}\mathrm{to}$$$$\left(1\right)219$$$$\left(2\right)200$$$$\left(3\right)220$$$$\left(4\right)221$$ Answered…

Question Number 84029 by mathmax by abdo last updated on 08/Mar/20 $$letf\left(x\right)=e^{-nx}ln(2+x^2)withnintegrnatural$$$$1)calculste{f}^{\left(n\right)}\left(x\right)and{f}^{\left(n\right)}\left(0\right)$$$$2)developpfatintegrserie$$$$\left.\mathrm{3}\right){find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{f}\left({x}\right){d}\:{and}\:\int_{\mathrm{0}} ^{\infty}…