tex]...

August 2022 1 6 Report

Найти D(у), если:
а)[tex]y=4^{4}-5x-1[/tex]
b)[tex]y=\sqrt{-x^{2}-4x+5 }[/tex]
c)[tex]y=\frac{3-2^{4} }{x-3}[/tex]
d)[tex]y=\frac{x-1}{\sqrt{x^{2}-9 } }[/tex]

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Artem112

Verified answer

а)

$y=4^{4}-5x-1$

$D(y)=\mathbb{R}$

$y=\sqrt{-x^{2}-4x+5 }$

$-x^{2}-4x+5\geq 0$

$x^{2}+4x-5\leq 0$

$(x-1)(x+5)\leq 0$

$x\in[-5;\ 1]$

$D(y)=[-5;\ 1]$

$y=\dfrac{3-2^{4} }{x-3}$

$x-3\neq 0$

$x\neq 3$

$D(y)=(-\infty;\ 3)\cup(3;\ +\infty)$

$y=\dfrac{x-1}{\sqrt{x^{2}-9 } }$

$x^{2}-9>0$

$(x-3)(x+3)>0$

$x=(-\infty;\ -3)\cup(3;\ +\infty)$

$D(y)=(-\infty;\ -3)\cup(3;\ +\infty)$

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