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17 December, 15:48

An even function must always have what characteristic?

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  1. 17 December, 15:52
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    Answer: If the function f (x) is even, then f (x) = f (-x).

    Examples:

    1. f (x) = x² + 3

    f (-x) = (-x) ² + 3

    = x² + 3

    = f (x)

    Therefore f (x) is even.

    2. f (x) = 3x⁶ - 4x⁴ + 5x² + 1

    f (-x) = 3 (-x) ⁶ - 4 (-x) ⁴ + 5 (-x) ² + 1

    = 3x⁶ - 4x⁴ + 5x² + 1

    = f (x)

    Therefore f (x) is even.
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