Найти область определения функции: а) f(x) = √(3^(7x-2)-9) ; б) f(x) = log_0,7⁡〖(x^2-9)/(x+5)〗Срочно. Created by Imperatrix. algebra-ru

А)-------------[4/7]--------------------- ////////////////////// ∞ б) --- - ---(-5)------+-----(-3)----- - -----(3)-----+----- ///////////////// //////////// ∪ ∞

(x+5)〗Срочно...

Imperatrix @Imperatrix

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Найти область определения функции: а) f(x) = √(3^(7x-2)-9) ; б) f(x) = log_0,7⁡〖(x^2-9)/(x+5)〗
Срочно

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Luluput

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А)
$f(x)= \sqrt{3^{7x-2}-9}$
$3^{7x-2}-9 \geq 0$
$3^{7x-2}\geq 9$
$3^{7x-2}\geq 3^2$
${7x-2}\geq 2$
${7x}\geq 2+2$
${7x}\geq 4$
${x}\geq \frac{4}{7}$
-------------[4/7]---------------------
//////////////////////
$D(f)=[ \frac{4}{7};+$ ∞ $)$

б)
$f(x)=log_{0.7} \frac{x^2-9}{x+5}$
$\frac{x^2-9}{x+5} \ \textgreater \ 0$
$\frac{(x-3)(x+3)}{x+5} \ \textgreater \ 0$
$x-3=0$ $x+3=0$ $x+5=0$
$x=3$ $x=-3$ $x=-5$

--- - ---(-5)------+-----(-3)----- - -----(3)-----+-----
///////////////// ////////////
$D(f)=(-5;-3)$ ∪ $(3;+$ ∞ $)$

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