It is known that f (x) and G (x) are odd and even functions on (- A, a) respectively. It is proved that f (x) · g (x) is odd function on (- A, a) | Math enthusiast | Mathematical art

It is known that f (x) and G (x) are odd and even functions on (- A, a) respectively. It is proved that f (x) · g (x) is odd function on (- A, a)

It is proved that: since f (x) and G (x) are odd and even functions on (- A, a) respectively, ∀ x ∈ (- A, a), then f (- x) = - f (x), G (- x) = g (x).. f (- x) · g (- x) = - f (x) · g (x), f (x) · g (x) is an odd function on (- A, a)

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