найдите область определения функции1) f(x)=logx-1 ( x/9-x²)2)f(x)=log3-x ((x²-4)/x). Created by grelllalala. algebra-ru

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grelllalala @grelllalala

July 2022 1 5 Report

найдите область определения функции
1) f(x)=logx-1 ( x/9-x²)
2)f(x)=log3-x ((x²-4)/x)

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NNNLLL54

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Ответ:

$1)\ \ f(x)=log_{x-1}\Big(\dfrac{x}{9-x^2}\Big)\\\\\\OOF:\ \left\{\begin{array}{l}x-1>0\\x-1\ne 1\\\dfrac{x}{9-x^2}>0\end{array}\right\ \ \left\{\begin{array}{l}x>1\\x\ne 2\\\dfrac{x}{(3-x)(3+x)}>0\end{array}\right\ \ \left\{\begin{array}{l}x>1\\x\ne 2\\\dfrac{x}{(x-3)(x+3)}$

$\left\{\begin{array}{l}x\in (\ 1\, ;\, 2\ )\cup (\ 2\ ;+\infty \, )\\x\in (\, -\infty \, ;-3\, )\cup (\ 0\ ;\ 3\ )\end{array}\right\ \ \ \Rightarrow \ \ x\in (\ 1\ ;\ 2\ )\cup (\ 2\ ;\ 3\ )$

$2)\ \ f(x)=log_{3-x}\, \dfrac{x^2-4}{x}\\\\\\OOF:\ \ \left\{\begin{array}{l}3-x>0\\3-x\ne 1\\\dfrac{(x-2)(x+2)}{x}>0\end{array}\right\ \ \left\{\begin{array}{l}x$

1 votes Thanks 1

NNNLLL54 всё верно

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