Question

найти область определения

Answer 1

$y=log_x}(5x-x^2)+\frac{sin^{-1}1}{x}+\sqrt[3]{x}\\\\OOF:\; \; \left \{ {{x>0\; ,\; x\ne 1\; ,\; x\ne 0} \atop {5x-x^2>0}} \right. \\\\5x-x^2>0\; \; \to \; \; x^2-5x<0\; ,\; \; x(x-5)<0\; ,\\\\x_1=0\; ,\; x_2=5\; ,\; \; znaki:\; \; +++(0)---(5)+++\\\\x\in (0,5)\\\\\left \{ {{x>0\; ,\; x\ne 1} \atop {x\in (0,5)}} \right. \; \; \Rightarrow \; \; \; \underline {x\in (0,1)\cup (1,5)}$