Mathematics

If $f(x)$ is an odd function, then $| f(x) |$ is

an even function

SOLUTION
If $f(x)$ is an odd function,
$f(-x)=-f(x)$
Let $g(x)=|f(x)|$
$\Rightarrow$  $g(-x)=|f(-x)|$

$\Rightarrow$  $g(-x)=|-f(x)|$

$\Rightarrow$  $g(-x)=|-1||f(x)|$

$\Rightarrow$  $g(-x)=|f(x)|=g(x)$

$\therefore$  $|f(x)|$ is an even function.

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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