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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…