If f(x) = 3x + 1 and g(x) = x^2 + 2x, find x when f(g(x)) = 10

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  1. math_celebrity

    math_celebrity Administrator Staff Member

    If f(x) = 3x + 1 and g(x) = x^2 + 2x, find x when f(g(x)) = 10

    Evaluate f(g(x))
    f(g(x)) = 3(x^2 + 2x) + 1
    f(g(x)) = 3x^2 + 6x + 1

    When f(g(x)) = 10, we have
    10 = 3x^2 + 6x + 1

    Subtract 10 from each side:
    3x^2 + 6x - 9 = 0

    Divide each side of the equation by 3
    x^2 + 2x - 3 = 0

    Factor, we have: (x + 3)(x - 1) = 0
    So x is either 1 or -3

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