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Category: Algebra

The-coefficient-of-x-4-in-2-4x-3x-2-2-i-s-

Question Number 54024 by sandip123 last updated on 28/Jan/19 $$\mathrm{The}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{x}^{\mathrm{4}} \:\mathrm{in}\:\left(\mathrm{2}−\mathrm{4x}+\mathrm{3x}^{\mathrm{2}} \right)^{−\mathrm{2}} \mathrm{i}\:\mathrm{s}\:? \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 28/Jan/19 $$\left(\mathrm{2}−\mathrm{4}{x}+\mathrm{3}{x}^{\mathrm{2}} \right)^{−\mathrm{2}} \\…

2-x-4-solve-for-x-

Question Number 54013 by zambolly19 last updated on 27/Jan/19 $$\mathrm{2}^{\boldsymbol{\mathrm{x}}} =−\mathrm{4}.\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{x}} \\ $$ Answered by Smail last updated on 27/Jan/19 $${xln}\mathrm{2}={ln}\left(−\mathrm{4}\right) \\ $$$${x}=\frac{{ln}\left(\mathrm{4}{e}^{{i}\pi} \right)}{{ln}\mathrm{2}}=\frac{\mathrm{2}{ln}\mathrm{2}+{i}\pi}{{ln}\mathrm{2}}=\mathrm{2}+{i}\frac{\pi}{{ln}\mathrm{2}} \\…

If-f-x-x-x-D-f-domain-and-R-f-range-

Question Number 185054 by mnjuly1970 last updated on 16/Jan/23 $$ \\ $$$$\:\:\mathrm{I}{f}\:,\:\:\:{f}\left({x}\right)=\:\frac{{x}}{\lfloor\:{x}\:\rfloor}\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:\:\:\mathrm{D}_{\:{f}} \:=?\left({domain}\right)\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{and}\:\:\:\:\:\:\:\:\:\:\mathrm{R}_{\:{f}\:} =\:?\:\left({range}\:\right) \\ $$ Answered by mahdipoor last updated…

Let-a-lt-c-lt-b-such-that-c-a-b-c-If-f-R-R-is-a-function-satisfying-the-relation-f-x-a-f-x-b-f-x-c-for-all-x-R-then-a-period-of-f-is-A-b-a-B-2-b-a-

Question Number 119490 by Ar Brandon last updated on 25/Oct/20 $$\mathrm{Let}\:{a}<\mathrm{c}<\mathrm{b}\:\mathrm{such}\:\mathrm{that}\:\mathrm{c}−{a}=\mathrm{b}−\mathrm{c}.\:\mathrm{If}\:{f}:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{is}\:\mathrm{a} \\ $$$$\mathrm{function}\:\mathrm{satisfying}\:\mathrm{the}\:\mathrm{relation} \\ $$$$\:\:{f}\left(\mathrm{x}+{a}\right)+{f}\left(\mathrm{x}+\mathrm{b}\right)={f}\left(\mathrm{x}+\mathrm{c}\right)\:\:\mathrm{for}\:\mathrm{all}\:\mathrm{x}\in\mathbb{R} \\ $$$$\mathrm{then}\:\mathrm{a}\:\mathrm{period}\:\mathrm{of}\:{f}\:\mathrm{is} \\ $$$$\left(\mathrm{A}\right)\:\left(\mathrm{b}−{a}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{B}\right)\:\mathrm{2}\left(\mathrm{b}−{a}\right) \\ $$$$\left(\mathrm{C}\right)\:\mathrm{3}\left(\mathrm{b}−{a}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\mathrm{4}\left(\mathrm{b}−{a}\right) \\ $$ Terms of…

Let-a-gt-0-and-f-R-R-a-function-satisfying-f-x-a-1-2-3f-x-3f-x-2-f-x-3-1-3-for-all-x-R-Then-a-period-of-f-x-is-ka-where-k-is-a-positive-integer-whose-value-is-A-1-

Question Number 119483 by Ar Brandon last updated on 24/Oct/20 $$\mathrm{Let}\:{a}>\mathrm{0}\:\mathrm{and}\:{f}:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{a}\:\mathrm{function}\:\mathrm{satisfying} \\ $$$$\:\:\:\:\:{f}\left(\mathrm{x}+{a}\right)=\mathrm{1}+\left[\mathrm{2}−\mathrm{3}{f}\left(\mathrm{x}\right)+\mathrm{3}{f}\left(\mathrm{x}\right)^{\mathrm{2}} −{f}\left(\mathrm{x}\right)^{\mathrm{3}} \right]^{\mathrm{1}/\mathrm{3}} \\ $$$$\mathrm{for}\:\mathrm{all}\:\mathrm{x}\in\mathbb{R}.\:\mathrm{Then}\:\mathrm{a}\:\mathrm{period}\:\mathrm{of}\:{f}\left(\mathrm{x}\right)\:\mathrm{is}\:{ka}\:\mathrm{where}\:{k}\:\mathrm{is} \\ $$$$\mathrm{a}\:\mathrm{positive}\:\mathrm{integer}\:\mathrm{whose}\:\mathrm{value}\:\mathrm{is} \\ $$$$\left(\mathrm{A}\right)\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{B}\right)\mathrm{2}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{C}\right)\mathrm{3}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\mathrm{4} \\ $$ Answered by…