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If the minimum value of f(x)=x^2+18x+a is the same as the minimum value of f(f(x)), what is the max value of a?

  • Maths -

    df/dx = 2x+18
    dg/dx = (2f+18)(2x+18)

    df/dx=0 when x = -9
    dg/dx=0 when f = -9 or x = -9

    f = -9 means
    x^2+18x+a = -9
    x = -9±√(72-a)

    So, a <= 72

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