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Category: Set Theory

Let-f-R-R-such-as-f-xy-f-x-f-y-1-Prove-that-f-is-derivable-iff-f-is-derivable-at-x-1-2-Prove-that-if-so-f-x-Log-a-x-where-a-is-positive-value-to-precise-

Question Number 216532 by sniper237 last updated on 11/Feb/25 $${Let}\:{f}\::\mathbb{R}_{+} \rightarrow\mathbb{R}\:{such}\:{as}\:{f}\left({xy}\right)={f}\left({x}\right)+{f}\left({y}\right) \\ $$$$\left.\mathrm{1}\right)\:{Prove}\:{that}\:\:{f}\:{is}\:{derivable}\:{iff}\:\: \\ $$$${f}\:{is}\:{derivable}\:{at}\:{x}=\mathrm{1}. \\ $$$$\left.\mathrm{2}\left.\right)\:{Prove}\:{that}\:{if}\:{so},\:{f}\left({x}\right)={Log}_{{a}} {x}\right)\: \\ $$$${where}\:{a}\:{is}\:{positive}\:{value}\:{to}\:{precise} \\ $$ Answered by maths2…

given-that-are-the-roots-of-the-equation-3×2-x-5-0-from-the-equation-whose-roots-are-2-1-2-1-

Question Number 216355 by jikansamu last updated on 05/Feb/25 $${given}\:{that}\:\varphi,\beta\:{are}\:{the}\:{roots}\:{of}\:{the}\:{equation}\:\mathrm{3}{x}\mathrm{2}−{x}−\mathrm{5}=\mathrm{0}\:{from}\:{the}\:{equation}\:{whose}\:{roots}\:{are}\:\mathrm{2}\varphi−\mathrm{1}/\beta,\mathrm{2}\beta−\mathrm{1}/\varphi \\ $$ Commented by AntonCWX last updated on 05/Feb/25 $${Please}\:{make}\:{sure}\:{to}\:{have}\:{your}\:{question}\:{typed}\:{neatly}\:{and}\:{in}\:{quality}. \\ $$ Answered by AntonCWX…

Let-A-x-R-x-2-lt-4-and-B-y-Q-y-gt-3-find-A-B-

Question Number 211643 by MrGaster last updated on 15/Sep/24 $$\mathrm{Let}\:\boldsymbol{{A}}=\left\{\boldsymbol{{x}}\:\in\:\mathbb{R}\mid\boldsymbol{{x}}^{\mathrm{2}} <\mathrm{4}\right\}\mathrm{and} \\ $$$$\boldsymbol{{B}}=\left\{\boldsymbol{{y}}\:\in\:\mathbb{Q}\mid\boldsymbol{{y}}>−\mathrm{3}\right\}\mathrm{find}\:\boldsymbol{{A}}\cap\boldsymbol{{B}} \\ $$ Answered by Faetmaaa last updated on 15/Sep/24 $${A}=\left(−\mathrm{2},\:\mathrm{2}\right) \\ $$$${B}=\boldsymbol{\mathrm{Q}}\cap\left(−\mathrm{3},\:\infty\right)…

Q-Choose-at-least-some-members-frome-the-set-A-14-15-20-22-23-28-so-that-whith-confidence-includes-three-consecutive-members-

Question Number 209746 by MM42 last updated on 21/Jul/24 $$\left.{Q}\right){Choose}\:{at}\:{least}\:{some}\:{members} \\ $$$${frome}\:{the}\:{set}\:{A}=\left\{\mathrm{14},\mathrm{15},…,\mathrm{20},\mathrm{22},\mathrm{23},…,\mathrm{28}\right\} \\ $$$${so}\:{that}\:{whith}\:{confidence}\:\:{includes}\:{three}\:{consecutive} \\ $$$${members}? \\ $$ Commented by MM42 last updated on 20/Jul/24…