Question

Найдите область определения функции 1) y=$\sqrt{x} + \sqrt{x-4}$ , 2) y=$\sqrt{x(x-4)}$

Answer 1

$y= \sqrt{x}+ \sqrt{x-4} \\ \left \{ {{x \geq 0} \atop {x-4 \geq 0}} \right. \\ \left \{ {{x \geq 0} \atop {x\geq 4}} \right. \\ x\geq4$
x∈[4;+∞)

$y= \sqrt{x(x-4)} \\ x(x-4) \geq 0 \\ x_1=0,x_2=4$
x∈(-∞;0]V[4;+∞)