If the domain of F (x) is symmetric about the origin, then f (x) times f (- x) is an even function How to prove it

Let f (x) = f (x) * f (- x), then the domain of F (x) is the same as that of F (x)
Because f (- x) = f (- x) * f [- (- x)] = f (x) * f (- x) = f (x)
So f (x) is an even function
And f (x) = f (x) * f (- x)
Therefore, f (x) * f (- x) is an even function

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