Math

How can I find the domain of g(x)=ln(2+x-x^2)? Can you show me step by step?

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  1. remember we can only take logs of positive numbers, so
    x^2 + x + 2 > 0

    If we consider the graph of
    y = -x^2 + x + 2, we have a parabola which opens downwards.
    So the domain of the original g(x) would be all those values of x for which the parabola is positive, that is, all those values of x for which the parabola lies above the x - axis.
    the x - intercepts are:
    y = (2-x)(1+x)
    so the zeros are x = 2 and x = -1

    so the domain is:
    -1 < x < 2 , (all the values between -1 and 2, excluding the end-values)

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    posted by Reiny

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