Question

Пожалуйста! Знайдіть область визначення функції / Найдите область определения функции.

Answer 1

$\displaystyle\bf\\y=\sqrt{5x+1} -\frac{6}{\sqrt{4+11x-3x^{2} } } \\\\\\\left \{ {{5x+1\geq 0} \atop {4+11x-3x^{2} >0}} \right. \\\\\\1)\\\\5x+1\geq 0\\\\5x\geq -1\\\\x\geq -0,2\\\\\\2)\\\\4+11x-3x^{2} >0\\\\3x^{2} -11x-4<0\\\\3x^{2} -11x-4=0\\\\D=(-11)^{2} -4\cdot 3\cdot(-4)=121+48=169=13^{2} \\\\\\x_{1} =\frac{11-13}{6} =-\frac{1}{3} \\\\\\x_{2} =\frac{11+13}{6} =4\\\\\\3x^{2} -11x-4=3\Big(x+\frac{1}{3}\Big )\Big(x-4\Big)\\\\\\\Big(x+\frac{1}{3}\Big )\Big(x-4\Big)<0$

+ + + + + (- 1/3) - - - - - (4) + + + + +

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$\displaystyle\bf\\x\in\Big[-0,2 \ ; \ 4\Big)$