Category: Algebra

Question Number 208381 by hardmath last updated on 14/Jun/24 $$\mathrm{g}\left(\mathrm{x}\right)={\mathrm{lnx}}^2$$$$\mathrm{f}\left(\mathrm{x}\right)=\sqrt[3]{\mathrm{x}+25}$$$$\mathrm{Find}:\underset{\mathbf{x}\to \mathbf{e}}{\lim }(\mathrm{f}\left(\mathrm{g}\left(\mathrm{x}\right)\right)=?$$ Answered by A5T last updated on 14/Jun/24 $${f}\left({g}\left({x}\right)\right)=\sqrt[{\mathrm{3}}]{{ln}\left({x}^{\mathrm{2}}…

Question Number 208370 by lmcp1203 last updated on 14/Jun/24 $$if\left(fof\right)\left(x\right)=f\left(x\right)+xandf\left(1\right)=1$$$$findfofofofofofofofofof\left(1\right)$$ Commented by A5T last updated on 14/Jun/24 $$f\left(f\left(x\right)\right)=f\left(x\right)+x\Rightarrow f\left(f\left(1\right)\right)=f\left(1\right)+1$$$$\Rightarrow{f}\left(\mathrm{1}\right)={f}\left(\mathrm{1}\right)+\mathrm{1}\Rightarrow\mathrm{1}\overset{?} {=}\mathrm{0}…

Question Number 208342 by hardmath last updated on 13/Jun/24 $$\mathrm{a},\mathrm{b},\mathrm{c}\in \mathbb{N}$$$$\mathrm{x}=4(2\mathrm{a}+5)=6(\mathrm{b}+9)=9(\mathrm{c}-1)$$$$\mathrm{find}:\mathbf{min}(\mathrm{x}+\mathrm{a}+\mathrm{b}+\mathrm{c})=?$$ Answered by A5T last updated on 13/Jun/24 $${c}=\frac{\mathrm{6}\left({b}+\mathrm{9}\right)}{\mathrm{9}}+\mathrm{1}=\frac{\mathrm{2}{b}}{\mathrm{3}}+\mathrm{7}\Rightarrow{b}=\mathrm{3}{k} \…

Question Number 208282 by hardmath last updated on 10/Jun/24 $$\mathrm{If}\cos \alpha -\cos \beta =\frac{1}{5}\sin \alpha +\sin \beta =\frac{1}{2}$$$$\mathrm{Find}\cos (\alpha +\beta )=?$$ Commented by mr W last updated on 12/Jun/24 $$whatyouwrotemeans$$$$\mathrm{cos}\alpha−\mathrm{cos}\beta\:=\frac{\mathrm{1}}{\mathrm{2}}…

Question Number 208259 by hardmath last updated on 09/Jun/24 Answered by cherokeesay last updated on 09/Jun/24 Answered by mr W last updated on 09/Jun/24 Commented…