Question

Указать область определения

Answer 1

$y=\frac{x^3}{-x^2+2|x|-1}\\\\OOF:\; \; -x^2+2|x|-1\ne 0\; \; \Rightarrow \; \; -(x^2-2|x|+1)\ne 0\; ,\\\\x^2-2|x|+1\ne 0\; ,\\\\x^2=|x|^2\; ,\; \; |x|^2-2|x|+1=(|x|-1)^2\ne 0\; \Rightarrow \; \; |x|-1\ne 0\; ,\\\\|x|\ne 1\; \; \Rightarrow \; \; x\ne -1\; \; i\; \; x\ne 1\\\\D(y)=(-\infty ,-1)\cup (-1,1)\cup (1,+\infty )$