Question

найдите область определения функции​

Answer 1

Ответ:

$y=\sqrt{5x+1}-\dfrac{6}{\sqrt{4+11x-3x^2}}\\\\\\OOF:\ \left\{\begin{array}{l}5x+1\geq 0\\4+11x-3x^2>0\end{array}\right\ \ \left\{\begin{array}{l}5x\geq -1\\3x^2-11x-4<0\end{array}\right\\\\\\3x^2-11x-4=0\ \ ,\ \ D=169\ \ ,\ \ x_1=-\dfrac{1}{3}\ ,\ x_2=4$

$\left\{\begin{array}{l}\ x\geq -\dfrac{1}{5}\\3(x+\frac{1}{3})(x-4)<0\end{array}\right\ \ \left\{\begin{array}{l}x\geq -\dfrac{1}{5}\\x\in (-\frac{1}{3} \, ;\, 4\, )\end{array}\right\ \ \ \Rightarrow \ \ \ x\in \Big(-\dfrac{1}{5}\ ;\ 4\ \Big)$