Question

Найдите область определения функции :
$y= frac{ sqrt{x+12} }{ x^{2-1} }$
$y= frac{x- sqrt{-x^{2}-7x+8 } }{1+ sqrt{x+3} }$

Answer 1

$y= frac{ sqrt{x+12} }{ x^{2-1} }= frac{ sqrt{x+12} }{ x } \ left { {{ x+12 geq 0} atop {x neq 0}} right. \ left { {{ x geq -12} atop {x neq 0}} right. \ xin(-12; 0)cup(0; +infty)$

$y= frac{x- sqrt{-x^{2}-7x+8 } }{1+ sqrt{x+3} } \ left { {{-x^{2}-7x+8 geq 0} atop {x+3 geq 0}} right. \ left { {{x^2+7x-8 leq 0} atop {x geq -3}} right. \ left { {{-8 leq x leq 1} atop {x geq -3}} right. \ -3 leq x leq 1$