Is $x\log\bigl(\cos(x)\bigr)$ an even or odd function?

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Is $x\log\bigl(\cos(x)\bigr)$ an even or odd function?

$$f(-x)=-x\log\bigl(\cos(-x)\bigr)=-x\log\bigl(\cos(x)\bigr)=-f(x)$$

So it seems an odd function and i've tried to draw the graph too.

But the suggested solution in my book says that it is an even function.

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1 Answer

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Yes, it is an odd function and your argument is correct.

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