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