Category: Relation and Functions

Question Number 21491 by dioph last updated on 24/Sep/17 $$\mathrm{If}Y\mathrm{is}\mathrm{a}\mathrm{non}-\mathrm{void}\mathrm{set},\mathrm{define}{Y}^T\mathrm{to}\mathrm{be}$$$$\mathrm{the}\mathrm{collection}\mathrm{of}\mathrm{all}\mathrm{functions}\mathrm{with}$$$$\mathrm{domain}T\mathrm{and}\mathrm{range}Y.\mathrm{Show}\mathrm{that}$$$$\mathrm{if}T\mathrm{and}Y\mathrm{are}\mathrm{finite}\mathrm{sets}\mathrm{with}m\mathrm{and}$$$$n\mathrm{elements},\mathrm{then}{Y}^T\mathrm{has}{n}^m\mathrm{elements}.$$ Terms of…

Question Number 86962 by abdomathmax last updated on 01/Apr/20 $$calculste{\int }_0^1{x}^{2}ln\left(x\right)ln(1-x)dx$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 86958 by abdomathmax last updated on 01/Apr/20 $$calculate\sum _{n=1}^{\mathrm{\infty }}\frac{{(-1)}^n}{n^3{(n+1)}^2}$$ Commented by mathmax by abdo last updated on…

Question Number 152151 by john_santu last updated on 26/Aug/21 Answered by Rasheed.Sindhi last updated on 26/Aug/21 $$f\left(x\right)=\frac{ax+b}{cx+d}$$$$\bullet f\left(f\left(x\right)\right)=\frac{a\left(\frac{ax+b}{cx+d}\right)+b}{c\left(\frac{ax+b}{cx+d}\right)+d}=x$$$$=\frac{a(ax+b)+b(cx+d)}{c(ax+b)+d(cx+d)}=x$$$${x}=\mathrm{0}:\:\frac{{ab}+{bd}}{{bc}+{d}^{\mathrm{2}} }=\mathrm{0} \…

Question Number 86406 by mathmax by abdo last updated on 28/Mar/20 $$let\overrightarrow{u}=\overrightarrow{i}-\overrightarrow{j}+\overrightarrow{k}and\overrightarrow{v}=2\overrightarrow{i}+\overrightarrow{j}+3\overrightarrow{k}$$$$(o,i,j,k)orthonormal$$$$\left.\mathrm{1}\right)\:{calculate}\:\:\mid\mid\overset{\rightarrow} {{u}}\mid\mid\:\:,\mid\mid\overset{\rightarrow}…