Category: Relation and Functions

Question Number 214644 by asifumer658 last updated on 14/Dec/24 $$\frac{-6}{7}/\frac{-7}{6}$$ Answered by Frix last updated on 17/Dec/24 $$\frac{-6}{7}/\frac{-7}{6}=(-\frac{6}{7})/(-\frac{7}{7})=(-\frac{6}{7})\times (-\frac{6}{7})=$$$$=\frac{36}{49}$$ Terms…

Question Number 212518 by efronzo1 last updated on 16/Oct/24 $$\cancel{\underbrace{\downharpoonleft }\underset{―}{}}$$ Answered by golsendro last updated on 16/Oct/24 $$\cancel{\underset{―}{\underbrace{\pm }}}={(\mathrm{x}-\mathrm{a})}^2+\mathrm{a}$$$$\:\:\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)=\:\sqrt{\mathrm{x}−\mathrm{a}}\:+\mathrm{a}\:…

Question Number 209707 by alcohol last updated on 19/Jul/24 $$a,b\in \mathbb{C}:a\stackrel{-}{b}+b=0f:z^{\prime }=a\stackrel{-}{z}+b$$$$suchthatf\left(M\right)=M^{\prime }$$$$1.let{z}_A=zand{z}_{A^{\prime }}=z^{\prime }andf\left(A\right)=A$$$$showthat2Re\left(\stackrel{-}{bz}\right)=b\stackrel{-}{b}$$$$\left({A}\:{is}\:{the}\:{set}\:{of}\:{invariant}\:{points}\:{and}\right. \…

Question Number 208431 by alcohol last updated on 15/Jun/24 $$h_a\left(x\right)=e^{-x}+{ax}^2$$$$showthat{h}_{a}admitsaminimumin\mathbb{R}$$ Answered by mathzup last updated on 15/Jun/24 $${cas}\:\mathrm{1}\:\:\:\:\:\:{a}>\mathrm{0}…

Question Number 208103 by depressiveshrek last updated on 05/Jun/24 $$\mathrm{Find}\inf \{\frac{m}{n}\mid m,n\in \mathbb{N},m<n-2\}$$ Answered by A5T last updated on 05/Jun/24 $$Sincem,n\in \mathbb{N},\frac{m}{n}>0,so0isalowerbound.$$$$\frac{m}{n}⩾\frac{1}{n}and\frac{1}{n}isintheset.$$$${For}\:{any}\:\epsilon>\mathrm{0},\:{one}\:{can}\:{always}\:{find}\:{n}\:{such}\:{that} \…