Question

Найдите область определения функции f(x)=√log внизу0,2далее дробь2x-10/x+11 и все это под корнем

Answer 1

$f(x)=\sqrt{log_{0,2}\frac{2x-10}{x+11}}\\\\OOF:\; \left \{ {{x+11\ne 0} \atop {\frac{2x-10}{x+11}>0,\; log_{0,2}\frac{2x-10}{x+11} \geq 0}} \right. \; \left \{{ x\ne -11} \atop {\frac{2(x-5)}{x+11}>0} ,{\frac{2(x-5)}{x+11} \leq 1}} \right. \\\\\frac{2(x-5)}{x+11}>0:\; \; +++(-11)---(5)+++\\\\x\in (-\infty,-11)U(5,+\infty)\\\\\frac{2(x-5)}{x+11}-1 \leq 0,\; \frac{2x-10-x-11}{x+11} \leq 0,\; \frac{x-21}{x+11} \leq 0,\\\\+++(-11)---(21)+++\\\\x\in (-11,21]\\\\Otvet:\; x\in (5,21]$