Category: Relation and Functions

Question Number 199781 by cortano12 last updated on 09/Nov/23 $$$$ Answered by qaz last updated on 09/Nov/23 $$f\left(x\right)=\frac{2(1-2x)}{x(1-x)}-f\left(\frac{1}{1-x}\right)$$$$=\frac{2(1-2x)}{x(1-x)}-(\frac{2(1-\frac{2}{1-x})}{\frac{1}{1-x}(1-\frac{1}{1-x})}-f\left(\frac{1}{1-\frac{1}{1-x}}\right))$$$$=\frac{\mathrm{2}\left(\mathrm{1}−\mathrm{2}{x}\right)}{{x}\left(\mathrm{1}−{x}\right)}−\frac{\mathrm{2}\left(\mathrm{1}+{x}\right)\left(\mathrm{1}−{x}\right)}{{x}}+{f}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}}\right) \…

Question Number 198541 by HomeAlone last updated on 21/Oct/23 $$s1=Abgdeeezdii/ii\mathrm{♮}\gg i$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 198178 by universe last updated on 13/Oct/23 $$f(xf\left(y\right)+x)=xy+f\left(x\right)$$$$f:\mathbb{R}\to \mathbb{R}$$$$f\left(x\right)=?$$ Answered by Rasheed.Sindhi last updated on 13/Oct/23 $${Let}\:{f}\left({x}\right)={ax}+{b} \…

Question Number 198065 by giovi last updated on 09/Oct/23 $$2^x+9+2^x=40$$ Answered by a.lgnaoui last updated on 09/Oct/23 $$2^{\mathrm{x}+1}=31\Rightarrow (\mathrm{x}+1)\ln 2=\ln 31$$$$\:\:\mathrm{x}=\frac{\mathrm{ln31}}{\mathrm{ln2}}−\mathrm{1}\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{x}}=\frac{\boldsymbol{\mathrm{ln}}\mathrm{31}−\boldsymbol{\mathrm{ln}}\mathrm{2}}{\boldsymbol{\mathrm{ln}}\mathrm{2}}…

Question Number 197132 by Erico last updated on 08/Sep/23 $${\underset{0}{\int }}^{+\mathrm{\infty }}{\left(\frac{\ln (\mathrm{t}+\sqrt{1+{\mathrm{t}}^2})}{\mathrm{t}}\right)}^2=\frac{{\pi }^2}{2}$$ Commented by mnjuly1970 last updated on 09/Sep/23 $$\:\:\:\:{ti}\:{tok}\:{agha}\:{sardool}\:..…