Question

Найдите область определения функций
f (x)= корень х^2+3х+4/х-3

Answer 1

$f(x)= \sqrt{ \frac{x^2+3x-4}{x-3} } \\ \\ \left \{ {{x-3 \neq 0} \atop { \frac{x^2+3x-4}{x-3} \geq 0}} \right. \\ \\ D=9+16=25; x_{1} =(-3-5)/2=-4; x_{2} =(-3+5)/2=1 \\ \\ \left \{ {{x \neq 3} \atop { \frac{(x-1)(x+4)}{x-3} \geq 0}} \right. \\ \\ ---[-4]+++[1]----(3)++++ \\ \\ x\in[-4;1]U(3;+oo)$