tex]...

June 2022 1 47 Report

Докажите, что является чётной функция у = f(x)

1)
[tex]f(x) = x {}^{2} + \sin(x) {}^{2} [/tex]
2)
[tex]f(x) = (2 - x {}^{2} ) \sin(x) {}^{2} - 5[/tex]

Answers & Comments

sharofat0

Verified answer

Ответ:

Докажите четность функции.

Объяснение:

$f(x) = {x }^{2} + sin( {x)}^{2}$

$sin( {x)}^{2} = sin( { - x)}^{2}$

==>

$f( - x) = ( { - x)}^{2} + sin {( - x)}^{2} =$

$= {x}^{2} + sin( {x})^{2}$

==>

$f( - x) = f(x)$

==>

Функция четная.

$f(x) = (2 - {x}^{2} )sin( {x})^{2} - 5$

$2 - {x}^{2} = 2 - ( { - x})^{2} = 2 - {x}^{2}$

$sin {(x})^{2} = sin( { - x})^{2}$

==>

$f( - x) = (2 - {x}^{2} )sin( {x}) ^{2} - 5 =$

$= (2 - {( - x})^{2} )sin( { - x})^{2} - 5 =$

$= (2 - {x}^{2} )sin( {x})^{2} - 5$

==>

$f( - x) = f(x)$

==>

Функция четная.

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