Category: Relation and Functions

Question Number 128496 by mathmax by abdo last updated on 07/Jan/21 $$\mathrm{calculate}\mathrm{A}=\frac{1}{{(2-\sqrt{6})}^4}+\frac{1}{{(2+\sqrt{6})}^4}$$ Commented by liberty last updated on 08/Jan/21 $$\frac{\left(\mathrm{2}−\sqrt{\mathrm{6}}\right)^{\mathrm{4}} +\left(\mathrm{2}+\sqrt{\mathrm{6}}\right)^{\mathrm{4}}…

Question Number 128425 by bramlexs22 last updated on 07/Jan/21 $$\mathrm{If}\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}+\tan \mathrm{x}\mathrm{and}\mathrm{f}\mathrm{is}\mathrm{inverse}$$$$\mathrm{of}\mathrm{g},\mathrm{then}{\mathrm{g}}^{\prime }\left(\mathrm{x}\right)\mathrm{is}\mathrm{equal}\mathrm{to}$$$$\left(\mathrm{a}\right)\frac{1}{1+{(\mathrm{g}\left(\mathrm{x}\right)-\mathrm{x})}^2}\left(\mathrm{b}\right)\frac{1}{1-{(\mathrm{g}\left(\mathrm{x}\right)-\mathrm{x})}^2}$$$$\left(\mathrm{c}\right)\frac{1}{2+{(\mathrm{g}\left(\mathrm{x}\right)-\mathrm{x})}^2}\left(\mathrm{d}\right)\frac{1}{2-{(\mathrm{g}\left(\mathrm{x}\right)-\mathrm{x})}^2}$$ Answered by liberty…

Question Number 62882 by mathmax by abdo last updated on 26/Jun/19 $$letf\left(x\right)=ln\mid \frac{x-1}{x+1}\mid$$$$1)determine{D}_f$$$$2){calculatef}^{\left(n\right)}\left(x\right)and{f}^{\left(n\right)}\left(0\right)$$$$3)developpfatintegrserie$$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{−\frac{\mathrm{1}}{\mathrm{2}}} ^{\frac{\mathrm{1}}{\mathrm{2}}} {f}\left({x}\right){dx}\:. \…

Question Number 62879 by mathmax by abdo last updated on 26/Jun/19 $$calculatemin\sum _{0⩽i⩽nand0⩽j⩽n}(i+j)$$ Answered by mr W last updated on 26/Jun/19 $$\sum_{\mathrm{0}\leqslant{i}\leqslant{n}\:\:{and}\:\mathrm{0}\leqslant{j}\leqslant{n}} \:\left({i}+{j}\right)…

Question Number 128401 by bramlexs22 last updated on 07/Jan/21 $$\mathrm{Given}\mathrm{function}\mathrm{f}(x+1)+\mathrm{f}(x-1)=x^2$$$$\mathrm{then}{\mathrm{f}}^{-1}\left(x\right)=?$$$$\left(A\right)\pm \sqrt{1-2x};x⩽\frac{1}{2}$$$$\left(B\right)\pm \sqrt{x+2};x⩾-2$$$$\left(C\right)\pm \sqrt{2x+1};x⩾-\frac{1}{2}$$$$\left(D\right)\pm \sqrt{3x-1};x⩾\frac{1}{3}$$$$\left(E\right)\pm \sqrt{2x-1};x⩾\frac{1}{2}$$…