Category: Relation and Functions

Question Number 2253 by 123456 last updated on 11/Nov/15 $$f_n:[0,1]\to [0,1],g:[0,1]\to [0,1]$$$$f_{n+1}\left(x\right)=g\left[f_n\left(x\right)\right]+f_n\left[g\left(x\right)\right]$$$$f_0\left(x\right)=x$$$$f_4\left(x\right)=?$$$${g}\left({x}\right)={x}^{\mathrm{2}} ,{f}_{\mathrm{2}}…

Question Number 2187 by 123456 last updated on 07/Nov/15 $$f:\mathbb{N}\to \mathbb{N}$$$$f(n+m)=f\left(n\right)+\alpha m$$$$f\left(0\right)=k$$$$f\left(n\right)=?$$ Answered by prakash jain last updated on…

Question Number 133168 by bemath last updated on 19/Feb/21 Answered by floor(10²Eta[1]) last updated on 19/Feb/21 $$\mathrm{x}\to 1-\frac{1}{\mathrm{x}}$$$$\left(\mathrm{I}\right):\mathrm{f}\left(\frac{\mathrm{x}}{\mathrm{x}-1}\right)+\mathrm{f}\left(\frac{1}{\mathrm{x}}\right)=\frac{\mathrm{x}-1}{\mathrm{x}}$$$$\mathrm{but}\mathrm{f}\left(\frac{1}{\mathrm{x}}\right)=\mathrm{x}-\mathrm{f}(1-\mathrm{x}),\mathrm{so}$$$$\mathrm{f}\left(\frac{\mathrm{x}}{\mathrm{x}-1}\right)+\mathrm{x}-\mathrm{f}(1-\mathrm{x})=\frac{\mathrm{x}-1}{\mathrm{x}}$$$$\left(\mathrm{II}\right):\:\mathrm{f}\left(\frac{\mathrm{x}}{\mathrm{x}−\mathrm{1}}\right)−\mathrm{f}\left(\mathrm{1}−\mathrm{x}\right)=\frac{−\mathrm{x}^{\mathrm{2}}…

Question Number 133122 by abdomsup last updated on 19/Feb/21 $$let{V}_n=\sum _{k=0}^n\frac{1}{\sqrt{n^2+1}}$$$$findaewivalentof{V}_n(n⌣\mathrm{\infty })$$ Terms of Service Privacy Policy Contact:…

Question Number 67540 by mathmax by abdo last updated on 28/Aug/19 $$provethat\mid \mathrm{\Gamma }(\frac{1}{2}+it)\mid =\sqrt{\frac{2\pi }{e^{\pi t}+e^{-\pi t}}}$$$$and\mid \mathrm{\Gamma }(1+it)\mid =\sqrt{\frac{2\pi t}{e^{\pi t}-e^{-\pi t}}}$$ Commented by ~ À ®…