Найдите область определения функции. Created by fcb03. matematika-ru

Функция будет определена на промежутке x²+6x+3=0D=24x(x+7)=0x3=0; x4=-7 + - + - +-------------0-------------0-------------0-------------0------------> -7 -3-√6 -3+√6 0 xx∈(-7;-3-√6)∪(-3+√6;0)

Найдите область определения функции...

fcb03 @fcb03

July 2022 1 7 Report

Найдите область определения функции

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fadarm

Verified answer

Функция будет определена на промежутке
$\frac{x-3}{ x^{2} +7x}\ \textgreater \ 1$
$\frac{ x^{2} +6x+3}{ x^{2} +7x}\ \textless \ 0
$
x²+6x+3=0
D=24
$x_{1}= \frac{-6-2\sqrt{6} }{2}=-3- \sqrt{6}$
$x_{2}= \frac{-6+2\sqrt{6} }{2}=-3+ \sqrt{6}$

x(x+7)=0
x3=0; x4=-7

+ - + - +
-------------0-------------0-------------0-------------0------------>
-7 -3-√6 -3+√6 0 x

x∈(-7;-3-√6)∪(-3+√6;0)

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