Question

f(x)=корень -x^2+3x+4/x .Найти область определения

Answer 1

$f(x)=sqrt{frac{-x^2+3x+4}{x}}\\OOF:; ; frac{-x^2+3x+4}{x}geq 0; ; ,; ; ; frac{-(x+1)(x-4)}{x}geq 0; ; ,; ; frac{(x+1)(x-4)}{x}leq 0; ,\\znaki:; ; ---[-1; ]+++(0)---[; 4; ]+++\\xin D(y)=(-infty ,-1, ]cup (0,4; ]$

$P.S.; ; ; ; f(x)=frac{sqrt{-x^2+3x+4}}{x}\\OOF:; ; left { {{-x^2+3x+4geq 0} atop {xne 0qquad quad }} right. ; ; left { {{-(x+1)(x-4)geq 0} atop {xne 0qquad quad }} right.; ; left { {{(x+1)(x-4)leq 0} atop {xne 0qquad quad }} right.; ; left { {{xin [-1, ;, 4; ]} atop {xne 0qquad }} right. \\xin D(y)=[-1, ;, 0)cup (0, ;, 4; ]$