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

Question

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.

Answer 1

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