Mathematics

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


ANSWER

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
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