Category: Relation and Functions

Question Number 84448 by jagoll last updated on 13/Mar/20 $$5^{\frac{{\mathrm{x}}^2-7\mid \mathrm{x}\mid +10}{{\mathrm{x}}^2-6\mathrm{x}+9}}<1$$ Answered by john santu last updated on 13/Mar/20 $$\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{7}\mid\mathrm{x}\mid+\mathrm{10}}{\mathrm{x}^{\mathrm{2}}…

Question Number 18653 by Tinkutara last updated on 26/Jul/17 $$\mathrm{Solve}\mathrm{the}\mathrm{inequality},\mid x-1\mid +\mid x+1\mid <4$$ Answered by ajfour last updated on 26/Jul/17 $$\mathrm{If}\mathrm{x}<-1$$$$-(\mathrm{x}-1)-(\mathrm{x}+1)<4$$$$\Rightarrow\:\mathrm{2x}>−\mathrm{4}\:\:\mathrm{or}\:\:\mathrm{x}>\:−\mathrm{2} \…

Question Number 18574 by Tinkutara last updated on 25/Jul/17 $$\mathrm{The}\mathrm{maximum}\mathrm{value}\mathrm{of}f\left(x\right)=2-\mid x{\mid }^2$$$$-2x\mathrm{is}\mathrm{equal}\mathrm{to}$$$$\left(1\right)6$$$$\left(2\right)4$$$$\left(3\right)5$$$$\left(4\right)3$$ Answered by prakash…

Question Number 149551 by puissant last updated on 06/Aug/21 Answered by Olaf_Thorendsen last updated on 06/Aug/21 $$a_n=\mathrm{P}\left(n\right)={an}^2+bn+c$$$$\forall{n}\in\mathbb{N},\:{a}_{{n}+\mathrm{1}} \:=\:\mathrm{3}{a}_{{n}} −{n}^{\mathrm{2}} +{n} \…

Question Number 83956 by jagoll last updated on 08/Mar/20 $$\mathrm{for}\mathrm{x}\in \mathbb{R}\mathrm{satisfy}\mathrm{the}\mathrm{equation}$$$$\mathrm{f}\left(\mathrm{x}\right)+3\mathrm{x}\mathrm{f}\left(\frac{1}{\mathrm{x}}\right)=2(\mathrm{x}+1)$$$$\mathrm{find}\mathrm{f}\left(2019\right).$$ Commented by mr W last updated on 08/Mar/20 $$\mathrm{f}\left(\mathrm{x}\right)+\mathrm{3x}\:\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\:=\:\mathrm{2}\left(\mathrm{x}+\mathrm{1}\right)\:\:\:…\left({i}\right)…