Statement - 1: Function f ( x ) = sin ( x + 3 sin x ) is periodic Statement - 2: f ( g ( x )) is periodic if g ( x ) is periodic

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Clearly f ( x + 2 π ) = sin ( x + 2 π + 3 sin ( x + 2 π )) = sin ( x + 3 sin x ) = f ( x ) , so 2 π is a period and statement 1 is true. Statement 2 is true in general (a function of a periodic function is periodic), but here g ( x ) = x + 3 sin x is not periodic, so statement 2 does not explain statement 1.

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