Question

найдите область определения функции

Answer 1

$y=\frac{1}{\sqrt{250\cdot 5^{3-x}-2\cdot 5^{x-3}}}\\\\OOF:\; \; 250\cdot 5^{3-x}-2\cdot 5^{x-3}0\\\\250\cdot 5^3\cdot 5^{-x}-2\cdot 5^{x}\cdot 5^{-3}0\\\\t=5^{x}0\; \; \to \; \; \; 5^{-x}=t^{-1}=\frac{1}{t}\; \; ,\; \; \; \frac{250\cdot 125}{t}-\frac{2\, t}{125}0\; ,\\\\\frac{250\cdot 125\cdot 125-2t^2}{125\, t}0\; \; ,\\\\250\cdot 125^2-2t^2=0\; ,\; 125^3-t^2=0\; \; ,\\\\t^2=125^3\; \; ,\; \; t^2=(5^3)^3\; \; ,\; \; t^2=5^9\; \; ,\; \; t=\pm \sqrt{5^9}$

$\frac{(t-\sqrt{5^9})(t+\sqrt{5^9})}{t}0\qquad ---(-\sqrt{5^9})+++(0)---(\sqrt{5^9})+++\\\\t\in (-\sqrt{5^9},0)\cup (\sqrt{5^9},+\infty )\\\\t0\; \; \to \; \; 5^{x}\sqrt{5^9}\; \; ,\; \; 5^{x}5^{4,5}\; \; ,\; \; \underline {x4,5}\\\\\underline {\, x\in (\; 4,5\; ;+\infty )\; }$