Question Number 85500 by oustmuchiya@gmail.com last updated on 22/Mar/20 $${The}\:{function}\:{of}\:\boldsymbol{\mathrm{f}}\:{and}\:\boldsymbol{\mathrm{g}}\:{are}\:{defined}\:{by}\:\boldsymbol{\mathrm{f}}:\boldsymbol{\mathrm{g}}\rightarrow\frac{{x}}{\boldsymbol{\mathrm{b}}{x}−\mathrm{2}},\:{x}\:\neq\:\frac{\mathrm{2}}{\boldsymbol{\mathrm{b}}}\:{and}\:\boldsymbol{\mathrm{b}}\:\neq\:\mathrm{0},\:{where}\:\boldsymbol{\mathrm{a}}\:{and}\:\boldsymbol{\mathrm{b}}\:{are}\:{real}\:{numbers}\:\boldsymbol{\mathrm{g}}:\boldsymbol{\mathrm{x}}\:\rightarrow\mathrm{2}{x}−\mathrm{11} \\ $$$$\left({a}\right)\:{If}\:\boldsymbol{\mathrm{f}}\left(\mathrm{2}\right)=\:\frac{-\mathrm{1}}{\mathrm{2}}\:{and}\:\boldsymbol{\mathrm{f}}^{−\mathrm{1}} \left(\mathrm{1}\right)\:=\:-\mathrm{1},\:{find}\:\boldsymbol{\mathrm{a}}\:{and}\:\boldsymbol{\mathrm{b}}\:{and}\:{write}\:{down}\:{the}\:{expression}\:{for}\:\boldsymbol{\mathrm{f}}\:{in}\:{terms}\:{of}\:\boldsymbol{\mathrm{x}} \\ $$$$\left(\boldsymbol{\mathrm{b}}\right)\:\boldsymbol{\mathrm{F}}{ind}\:{the}\:{value}\:{of}\:\boldsymbol{\mathrm{x}}\:{for}\:{which}\:\boldsymbol{\mathrm{fg}}\left(\boldsymbol{\mathrm{x}}\right)=\:\frac{-\mathrm{1}}{\mathrm{2}} \\ $$ Answered by john santu last updated on 22/Mar/20…
Question Number 150967 by EDWIN88 last updated on 17/Aug/21 $${E}\left({x}+\frac{\mathrm{2}}{{x}}\right)=\frac{{x}^{\mathrm{3}} +\mathrm{1}}{{x}}\:+\frac{{x}^{\mathrm{3}} +\mathrm{8}}{\mathrm{2}{x}^{\mathrm{2}} }\:+\mathrm{3}\:, \\ $$$$\:{E}\left(\mathrm{2}\right)=? \\ $$ Answered by john_santu last updated on 17/Aug/21 $$\:\mathrm{E}\left(\mathrm{x}+\frac{\mathrm{2}}{\mathrm{x}}\right)=\frac{\mathrm{x}^{\mathrm{3}}…
Question Number 85425 by john santu last updated on 22/Mar/20 $${range}\:{of}\:{function} \\ $$$${y}\:=\:\frac{\mid{x}−\mathrm{1}\mid}{{x}+\mathrm{3}} \\ $$ Answered by john santu last updated on 22/Mar/20 $${for}\:{x}\:\geqslant\mathrm{1}\:\Rightarrow\:{y}\:=\:\frac{{x}−\mathrm{1}}{{x}+\mathrm{3}} \\…
Question Number 19811 by Joel577 last updated on 16/Aug/17 $$\mathrm{If}\:{f}\left({x}\right)\:=\:\left({x}\:+\mathrm{1}\right){g}\left({x}\right)\:−\:\mathrm{2}\:\mathrm{and}\:{g}\left(\mathrm{3}\right)\:=\:\mathrm{4} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{if}\:{f}\left({x}\right)\:\mathrm{divided}\:\mathrm{by}\: \\ $$$$\left({x}\:+\:\mathrm{1}\right)\left({x}\:−\:\mathrm{3}\right) \\ $$ Commented by myintkhaing last updated on 16/Aug/17 $$\mathrm{Since},\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\left(\mathrm{x}+\mathrm{1}\right)\mathrm{g}\left(\mathrm{x}\right)\:−\mathrm{2}\:\mathrm{and}\:\mathrm{g}\left(\mathrm{3}\right)\:=\:\mathrm{4} \\…
Question Number 85233 by jagoll last updated on 20/Mar/20 $$\mathrm{what}\:\mathrm{is}\:\mathrm{domain}\:\:\mathrm{of}\:\mathrm{x}\:\mathrm{for} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)+\mathrm{2f}\left(\mathrm{1}−\mathrm{x}\right)=\:\mathrm{x}^{\mathrm{2}} \\ $$ Commented by jagoll last updated on 20/Mar/20 $$\mathrm{replace}\:\mathrm{1}−\mathrm{x}\:\mathrm{by}\:\mathrm{x}\: \\ $$$$\mathrm{f}\left(\mathrm{1}−\mathrm{x}\right)+\mathrm{2f}\left(\mathrm{x}\right)\:=\:\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{2}} \:\left(\mathrm{ii}\right)…
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Question Number 85164 by mathmax by abdo last updated on 19/Mar/20 $${calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{arctan}\left(\frac{\mathrm{1}}{{n}^{\mathrm{2}} \:+{n}+\mathrm{1}}\right) \\ $$ Commented by Cmr 237 last updated on 19/Mar/20…
Question Number 85165 by mathmax by abdo last updated on 19/Mar/20 $${sove}\:\:\left({sin}^{\mathrm{2}} {x}\right)\:{y}^{'} \:\:+\left({cosx}\right){y}\:={x} \\ $$ Commented by mathmax by abdo last updated on 20/Mar/20…
Question Number 85163 by mathmax by abdo last updated on 19/Mar/20 $${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:{arctan}\left(\frac{\mathrm{1}}{{n}^{\mathrm{2}} \:+{n}}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 150626 by puissant last updated on 14/Aug/21 $${S}\left({x}\right)=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{ln}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right){x}^{{n}} \\ $$$${S}\left(−\mathrm{1}\right)=\:?.. \\ $$$${please}\:{help}.. \\ $$ Answered by puissant last updated on 14/Aug/21…