Category: Algebra

Question Number 147254 by Ar Brandon last updated on 19/Jul/21 $$\mathrm{Soient}\mathrm{a}\in ]0,1[\mathrm{et}\mathrm{b}\in \mathbb{R}.\mathrm{Soit}\mathrm{f}\mathrm{une}\mathrm{application}\mathrm{de}\mathbb{R}\mathrm{dans}\mathrm{lui}-\mathrm{m}\widehat{\mathrm{e}me},\mathrm{de}\mathrm{classe}{\mathrm{C}}^1,\mathrm{telle}\mathrm{que}\mathrm{pour}\mathrm{tout}\mathrm{r}\acute{\mathrm{e}el}$$$$\mathrm{x},\mathrm{f}\left(\mathrm{f}\left(\mathrm{x}\right)\right)=\mathrm{ax}+\mathrm{b}.$$$$$$$$1.\mathrm{Montrer}\mathrm{que}\mathrm{pour}\mathrm{tout}\mathrm{r}\acute{\mathrm{e}el}\mathrm{x},\mathrm{f}(\mathrm{ax}+\mathrm{b})=\mathrm{af}\left(\mathrm{x}\right)+\mathrm{b}.\mathrm{En}\mathrm{d}\acute{\mathrm{e}duire}\mathrm{que}\mathrm{pour}\mathrm{tout}\mathrm{r}\acute{\mathrm{e}el}\mathrm{x},$$$$\:\:\mathrm{f}\:'\left(\mathrm{ax}+\mathrm{b}\right)=\mathrm{f}\:'\left(\mathrm{x}\right).…

Question Number 81692 by Power last updated on 14/Feb/20 Commented by MJS last updated on 14/Feb/20 $$\mathrm{just}\mathrm{put}a=-b-c$$$$\Rightarrow \mathrm{answer}\mathrm{is}9$$ Terms of Service Privacy…

Question Number 147223 by mathlove last updated on 19/Jul/21 Commented by bramlexs22 last updated on 19/Jul/21 $$2^{3\mathrm{x}}+2^{\mathrm{x}}.3^{2\mathrm{x}}-2.3^{3\mathrm{x}}=0$$$$\:$$\{\begin{array}{l}{2}^{\mathrm{x}}=\mathrm{u}\\ 3^{\mathrm{x}}=\mathrm{v}\end{array}$$\:\Rightarrow\mathrm{u}^{\mathrm{3}}…

Question Number 81654 by peter frank last updated on 14/Feb/20 Commented by peter frank last updated on 14/Feb/20 $$weneedtoprove$$$${a}^{\mathrm{2}} {x}^{\mathrm{2}} +{b}^{\mathrm{2}} {y}={a}^{\mathrm{2}} \left({a}^{\mathrm{2}}…

Question Number 81655 by peter frank last updated on 14/Feb/20 Terms of Service Privacy Policy Contact: info@tinkutara.com