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What is the difference between (f(a)+f(b))/2 and f((a+b)/2)?

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  • Anonymous
    1 decade ago
    Favorite Answer

    [(f(a) + f(b)) / 2[ is the arithmetic mean of f(a) and f(b)

    f((a+b)/2) is the function/mapping f(x) applied to the arithmetic mean of a and b

  • 1 decade ago

    Let f(x) = x^2, a = 2, b = 4

    (f(a)+f(b))/2 = (4+16)/2 = 10

    f((a+b)/2) = f((2+4)/2) = f(3) = 9

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