Question

Y=√(3x^-x-14)/(x^2-9) найти область определения !

Answer 1

$y=\frac{\sqrt{3x^2-x-14}}{x^2-9}\\\\OOF:\; \; \left \{ {{3x^2-x-14 \geq 0} \atop {x^2-9\ne 0}} \right. \; \left \{ {{3(x+2)(x-\frac{7}{3}) \geq 0} \atop {x^2\ne 9}} \right. \; \left \{ {{x\in (-\infty ,-2\, ]\cup [\, \frac{7}{3},+\infty )} \atop {x\ne \pm 3}} \right. \; \; \to \\\\x\in (-\infty ,-3)\cup (-3,-2\, ]\cup [\frac{7}{3},3)\cup (3,+\infty )\\\\\\\star \; 3x^2-x-14=0\; ,\; \; D=169\; ,\; \; x_1=\frac{1-13}{6}=-2,\; x_2=\frac{1+13}{6}=\frac{7}{3}\\\\+++[-2\, ]---[\, \frac{7}{3}\, ]+++\\\\x\in (-\infty ,-2\, ]\cup [\, \frac{7}{3},+\infty )$