Category: Relation and Functions

Question Number 27081 by abdo imad last updated on 01/Jan/18 $$letgivef\left(x\right)=\frac{x}{4x^2-1}find{f}^{\left(n\right)}\left(x\right).$$ Answered by prakash jain last updated on 01/Jan/18 $${f}\left({x}\right)\frac{{x}}{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{1}}=\frac{\mathrm{1}}{\mathrm{4}}\left(\frac{\mathrm{1}}{\mathrm{2}{x}−\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{2}{x}+\mathrm{1}}\right)…

Question Number 27050 by Joel578 last updated on 01/Jan/18 Commented by Joel578 last updated on 01/Jan/18 $${(a+c)}^2-{(b+d)}^2=a^2+c^2+2ac-b^2-d^2-2bd$$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\left({a}^{\mathrm{2}}…

Question Number 92301 by jagoll last updated on 06/May/20 $$\mathrm{given}\mathrm{eq}\mathrm{of}\mathrm{line}$$$$\left(1\right)[\mathrm{x},\mathrm{y}]=[3,-2]+\mathrm{t}[4,-5]$$$$\left(2\right)[\mathrm{x},\mathrm{y}]=[1,1]+\mathrm{s}[7,\mathrm{k}]$$$$\mathrm{find}\mathrm{t}\mathrm{and}\mathrm{s}\mathrm{if}\left(1\right)\parallel \left(2\right)$$$$\mathrm{if}\left(1\right)\mathrm{\perp }\left(2\right)$$ Commented by jagoll last updated…

Question Number 92197 by jagoll last updated on 05/May/20 $$\mathrm{Given}\mathrm{L}\left(\mathrm{n}\right)=\{\begin{array}{l}0,\mathrm{if}\mathrm{n}=1\\ \mathrm{L}\lfloor \frac{\mathrm{n}}{2}\rfloor +1,\mathrm{if}\mathrm{n}>1\end{array}$$$$\mathrm{find}\mathrm{L}\left(25\right)$$ Commented by john santu last updated on 05/May/20 $$\mathrm{L}\left(25\right)=\mathrm{L}\left(12\right)+1$$$$=\:\left[\:\mathrm{L}\left(\mathrm{6}\right)\:+\:\mathrm{1}\:\right]\:+\mathrm{1}\:=\:\mathrm{L}\left(\mathrm{6}\right)\:+\mathrm{2}…

Question Number 26576 by gunawan last updated on 27/Dec/17 $$\mathrm{Find}\mathrm{all}f:\mathrm{R}\to \mathrm{R}\mathrm{such}\mathrm{that}$$$$f(x+f\left(x\right)+f\left(y\right))=f(y+f\left(x\right))+x+f\left(y\right)-f\left(f\left(y\right)\right)$$$$\mathrm{for}\mathrm{all}x,\mathrm{y}\in \mathrm{R}$$ Commented by prakash jain last updated on 27/Dec/17 $${f}\left({x}+{f}\left({x}\right)+{f}\left({y}\right)\right)={f}\left({y}+{f}\left({x}\right)+{x}+{f}\left({y}\right)−{f}\left({f}\left({y}\right)\right)\right)?\:…