Category: Relation and Functions

Question Number 10741 by okhema last updated on 24/Feb/17 $${a}\:{function}\:{f}\:{is}\:{defined}\:{by}\:{f}\left({x}\right)=\:\frac{{x}+\mathrm{3}}{{x}−\mathrm{1}},\:{x}\:{not}\:{equal}\:{to}\:\mathrm{1}.{determine}\:{whether}\:{f}\:{is}\:{bijective},{that}\:{is},{both}\:{one}\:{to}\:{one}\:{and}\:{onto} \\ $$$$ \\ $$ Answered by mrW1 last updated on 24/Feb/17 $${f}\left({x}\right)=\:\frac{{x}+\mathrm{3}}{{x}−\mathrm{1}}={y} \\ $$$${x}+\mathrm{3}={yx}−{y} \\…

Question Number 141774 by mathmax by abdo last updated on 23/May/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } }{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$ Answered by Dwaipayan Shikari last updated…

Question Number 76193 by abdomathmax last updated on 25/Dec/19 $${calculate}\:\int\:\:\left({x}^{\mathrm{2}} −\mathrm{1}\right){sh}\left(\mathrm{3}{x}\right){dx} \\ $$ Commented by benjo last updated on 25/Dec/19 $$\mathrm{sir}\:\:\mathrm{do}\:\mathrm{you}\:\mathrm{mean}\:\mathrm{sh}\left(\mathrm{3x}\right)\:=\mathrm{sinh}\:\left(\mathrm{3x}\right)? \\ $$ Commented by…

Question Number 141653 by Mathspace last updated on 21/May/21 $${what}\:{is}\:{condition}\:{to}\:{have} \\ $$$${log}\left(\:{I}\:+{A}\right)=\Sigma\:{a}_{{n}} {A}^{{n}} \\ $$$${and}\:{determine}\:{the}\:{sequence}\:\left({a}_{{n}} \right) \\ $$$${A}\:\in\:{M}_{{n}} \left({C}\right) \\ $$ Terms of Service Privacy…

Question Number 141568 by sarkor last updated on 20/May/21 Commented by Dwaipayan Shikari last updated on 20/May/21 $${Area}\:{between}\:{this}\:{curves} \\ $$$$\sqrt{{x}}={x}^{\mathrm{2}} \Rightarrow{x}=\mathrm{1}\:\left({Meeting}\:{point}\right) \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{x}}−{x}^{\mathrm{2}}…