Question

Найдите область определения функций

Answer 1

1)log(3)x>0

x>3^0

x>1

2)2-x>0;x<2 и x>0; x≠1

x=(0;1)U(1;2)

3)|x|≠2; x≠+-2

x=(-∞;-2)U(-2;2)U(2;+∞)

Answer 2

$1)\; \; y=log_{0,2}log_3x\\\\OOF:\; \; \left \{ {{log_3x>0} \atop {x>0}} \right. \; \left \{ {{x>1} \atop {x>0}} \right. \; \; \Rightarrow \; \; x>1\\\\x\in (1,+\infty )\\\\2)\; \; y=log_2(2-x)+2log_{x}5\\\\OOF:\; \; \left \{ {{2-x>0} \atop {x>0\; ,\; x\ne 1}} \right. \; \left \{ {{x<2} \atop {x>0\; ,\; x\ne 1}} \right. \; \; \Rightarrow \; \; x\in (0,1)\cup (1,2)\\\\3)\; \; y=\frac{1}{|x|-2}\\\\OOF:\; \; |x|-2\ne 0\; ,\; \; |x|\ne 2\; ,\; \; x\ne \pm 2\\\\x\in (-\infty ,-2)\cup (-2,2)\cup (2,+\infty )$