Category: Relation and Functions

Question Number 18416 by Tinkutara last updated on 20/Jul/17 $$\mathrm{The}\mathrm{number}\mathrm{of}\mathrm{integral}\mathrm{values}\mathrm{of}x$$$$\mathrm{which}\mathrm{satisfies}$$$$\frac{{(x-5)}^{10}{(x-13)}^{20}{(x-19)}^{13}}{{(x-10)}^{18}{(x-25)}^{19}}⩾0\mathrm{and}$$$$2⩽x⩽30\mathrm{are}$$$$\left(1\right)23$$$$\left(\mathrm{2}\right)\:\mathrm{24}…

Question Number 83662 by jagoll last updated on 05/Mar/20 $$\mathrm{if}\mathrm{f}\left(\mathrm{x}\right)=\sqrt{{\mathrm{x}}^2-1}\mathrm{and}\mathrm{g}\left(\mathrm{x}\right)=\frac{1}{\sqrt{{\mathrm{x}}^2-3}}$$$$\mathrm{find}\mathrm{domain}\mathrm{function}$$$$(\mathrm{g}\bullet \mathrm{f})\left(\mathrm{x}\right)$$ Commented by MJS last updated on 05/Mar/20…

Question Number 83539 by jagoll last updated on 03/Mar/20 $$\mathrm{what}\mathrm{is}\mathrm{range}\mathrm{of}\mathrm{function}$$$$\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{x}}{\sqrt{{\mathrm{x}}^2-1}}?$$ Commented by john santu last updated on 03/Mar/20 $$\mathrm{domain}\:\mathrm{x}^{\mathrm{2}} −\mathrm{1}>\mathrm{0}\:\Rightarrow\:\mathrm{x}<−\mathrm{1}\:\vee\mathrm{x}\:>\mathrm{1}…

Question Number 83420 by jagoll last updated on 02/Mar/20 $$\mathrm{find}\mathrm{range}\mathrm{x}\mathrm{of}\mathrm{function}$$$$\mathrm{x}-4\sqrt{\mathrm{y}}=2\sqrt{\mathrm{x}-\mathrm{y}}$$ Commented by mathmax by abdo last updated on 02/Mar/20 $${we}\:{have}\:\mathrm{0}\leqslant{y}\leqslant{x}\:\:\:\left({e}\right)\Rightarrow\left({x}−\mathrm{4}\sqrt{{y}}\right)^{\mathrm{2}} =\mathrm{4}\left({x}−{y}\right)\:\Rightarrow…

Question Number 83406 by jagoll last updated on 02/Mar/20 $$\mathrm{If}{\mathrm{u}}_1+{\mathrm{u}}_2+{\mathrm{u}}_3+\dots +{\mathrm{u}}_{\mathrm{n}}={2\mathrm{n}}^2+\mathrm{n}$$$$\mathrm{is}\mathrm{a}\mathrm{AP}.\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}$$$$\mathrm{u}_{\mathrm{1}} +\mathrm{u}_{\mathrm{2}} +\mathrm{u}_{\mathrm{3}} +…+\mathrm{u}_{\mathrm{2n}−\mathrm{2}} +\mathrm{u}_{\mathrm{2n}−\mathrm{1}} \:. \…