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

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