Пожалуйста помогите!!! найдите область определения. Created by kati70. algebra-ru

Пожалуйста помогите!!! найдите область определения...

kati70 @kati70

August 2022 1 4 Report

Пожалуйста помогите!!! найдите область определения

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NNNLLL54

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$y= \sqrt{log_2\, \frac{x+1}{2x-4}}\; \; \Rightarrow \; \; \left \{ {{log_2\, \frac{x+1}{2x-4} \geq 0} \atop {\frac{x+1}{2x-4}\ \textgreater \ 0}} \right.\\\\a)\; \; log_2\, \frac{x+1}{2x-4} \geq 0\; ,\; \; \frac{x+1}{2x-4} \geq 1\; ,\; \; \frac{x+1}{2x-4} -1\geq 0\; ,\frac{x+1-2x+4}{2x-4}\geq 0\\\\ \frac{-x+5}{2x-4}\geq 0\; ,\; \; \frac{x-5}{2x-4}\leq 0\; ,\\\\x-5=0\; ,\; x_1=5\; ;\; \; \; 2x-4=0\; ,\; x_2=2\\\\+++(2)---[\, 5\, ]+++\\\\x\in (2,5\, ]\\\\b)\; \; \frac{x+1}{2x-4}\ \textgreater \ 0\; ,\\\\x+1=0\; ,\; x_1=-1\; \; ;\; \; 2x-4=0\; ,\; x_2=2$

$+++(-1)---(2)+++\\\\x\in (-\infty -1)\cup (2,+\infty )\\\\c)\; \; \left \{ {{x\in (2,5\, ]} \atop {x\in (-\infty ,-1)\cup (2,+\infty )}} \right. \; \; \Rightarrow \; \; \; \underline {x\in (2,5\, ]}$

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