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Category: Relation and Functions

F-x-log-sin-x-cos-x-log-sin-2x-find-the-Domain-of-F-D-F-

Question Number 151742 by mnjuly1970 last updated on 22/Aug/21 $$\:\: \\ $$$$\:\:\:\mathrm{F}\:\left({x}\:\right):=\:\frac{{log}\:\left({sin}\left({x}\right)\:+{cos}\:\left({x}\right)\right)}{{log}\:\left({sin}\left(\mathrm{2}{x}\right)\right)} \\ $$$$\:\:{find}\:\:\:{the}\:{Domain}\:{of}\:\:\:\:\mathrm{F}\:… \\ $$$$\:\:\:\mathrm{D}_{\:\mathrm{F}} \:=? \\ $$ Answered by mindispower last updated on…

Given-that-f-x-2x-7-8-and-g-x-3x-6-6-find-a-g-6-b-f-1-x-c-the-value-of-x-if-f-x-g-x-

Question Number 86189 by oustmuchiya@gmail.com last updated on 27/Mar/20 $${Given}\:{that}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\frac{\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{7}}{\mathrm{8}}\:{and}\:\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{x}}\right)=\:\frac{\mathrm{3}\boldsymbol{\mathrm{x}}−\mathrm{6}}{\mathrm{6}},\:{find} \\ $$$$\left(\mathrm{a}\right)\:\boldsymbol{\mathrm{g}}\left(\mathrm{6}\right),\:\left(\mathrm{b}\right)\boldsymbol{\mathrm{f}}^{−\mathrm{1}} \left(\boldsymbol{\mathrm{x}}\right)\:\:\:\left(\mathrm{c}\right)\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\boldsymbol{\mathrm{x}}\:{if}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{x}}\right) \\ $$ Answered by Kunal12588 last updated on 27/Mar/20 $$\left({a}\right)\:{g}\left(\mathrm{6}\right)=\frac{\mathrm{18}−\mathrm{6}}{\mathrm{6}}=\mathrm{2} \\ $$$$\left({b}\right)\:{f}^{−\mathrm{1}}…

If-x-1-f-x-f-1-x-1-x-1-find-f-x-

Question Number 86160 by jagoll last updated on 27/Mar/20 $$\mathrm{If}\:\left(\mathrm{x}−\mathrm{1}\right)\:\mathrm{f}\left(\mathrm{x}\right)\:+\:\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\:=\:\frac{\mathrm{1}}{\mathrm{x}−\mathrm{1}} \\ $$$$\mathrm{find}\:\mathrm{f}\left(\mathrm{x}\right)\: \\ $$ Commented by john santu last updated on 27/Mar/20 $${replace}\:{x}\:{by}\:\frac{\mathrm{1}}{{x}} \\ $$$$\Rightarrow\left(\frac{\mathrm{1}}{{x}}−\mathrm{1}\right){f}\left(\frac{\mathrm{1}}{{x}}\right)+{f}\left({x}\right)=\:\frac{\mathrm{1}}{\frac{\mathrm{1}}{{x}}−\mathrm{1}}…

Given-that-f-x-8x-and-g-x-3x-2-4-find-a-f-1-x-b-an-expression-for-fg-x-c-value-of-x-which-fg-x-20-

Question Number 86129 by oustmuchiya@gmail.com last updated on 27/Mar/20 $${Given}\:{that}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\mathrm{8}\boldsymbol{\mathrm{x}}\:{and}\:\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{x}}\right)=\frac{\mathrm{3}\boldsymbol{\mathrm{x}}−\mathrm{2}}{\mathrm{4}},\:{find} \\ $$$$\left(\mathrm{a}\right)\:\boldsymbol{\mathrm{f}}^{−\mathrm{1}} \left(\boldsymbol{\mathrm{x}}\right)\:\:\:\left(\mathrm{b}\right)\:{an}\:{expression}\:{for}\:\boldsymbol{{fg}}\left(\boldsymbol{\mathrm{x}}\right) \\ $$$$\left(\mathrm{c}\right)\:{value}\:{of}\:\boldsymbol{\mathrm{x}}\:{which}\:\boldsymbol{\mathrm{fg}}\left(\boldsymbol{\mathrm{x}}\right)=\mathrm{20}\: \\ $$ Commented by jagoll last updated on 27/Mar/20 $$\left.\mathrm{a}\right)\:\mathrm{f}^{−\mathrm{1}}…

Tbe-function-f-and-g-are-defined-by-f-x-2x-3-and-g-x-3x-Find-a-f-1-x-b-gf-x-c-gf-2-

Question Number 86030 by oustmuchiya@gmail.com last updated on 26/Mar/20 $${Tbe}\:{function}\:\boldsymbol{\mathrm{f}}\:{and}\:\boldsymbol{\mathrm{g}}\:{are}\:{defined}\:{by}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\mathrm{2}\boldsymbol{\mathrm{x}}−\mathrm{3}\:{and}\:\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{x}}\right)=\mathrm{3}\boldsymbol{\mathrm{x}}. \\ $$$$\boldsymbol{\mathrm{F}}{ind}\:\left(\boldsymbol{\mathrm{a}}\right)\:\boldsymbol{\mathrm{f}}^{−\mathrm{1}} \left(\boldsymbol{\mathrm{x}}\right)\:\:\:\:\left(\boldsymbol{\mathrm{b}}\right)\:\boldsymbol{\mathrm{gf}}\left(\boldsymbol{\mathrm{x}}\right)\:\:\:\left(\boldsymbol{\mathrm{c}}\right)\:\boldsymbol{\mathrm{gf}}\left(\mathrm{2}\right) \\ $$ Commented by Rio Michael last updated on 26/Mar/20 $$\:{f}:\:{x}\:\rightarrow\:\mathrm{2}{x}−\mathrm{3}\:\:\:\mathrm{and}\:\mathrm{g}\::\:{x}\:\rightarrow\:\mathrm{3}{x} \\…

Determine-a-relation-between-the-coefficients-a-b-c-d-such-that-the-equation-ax-3-bx-2-cx-d-0-has-three-real-roots-with-a-pair-of-double-roots-

Question Number 20279 by ajfour last updated on 25/Aug/17 $${Determine}\:{a}\:{relation}\:{between}\:\:{the} \\ $$$${coefficients}\:\:\boldsymbol{{a}},\:\boldsymbol{{b}},\:\boldsymbol{{c}},\:\boldsymbol{{d}}\:{such}\:{that}\:{the} \\ $$$${equation}:\:\:{ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0} \\ $$$${has}\:{three}\:{real}\:{roots}\:\left({with}\:{a}\:{pair}\right. \\ $$$$\left.{of}\:{double}\:{roots}\right). \\ $$ Terms of Service…