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Which of the following expressions is defined for all integer values of z, such that (z^2) <9? I. (z+1)/z II. (z-4)/(z^2-4z+4) III. 18/(z^2-4z-5)
a) None b) I only c) II only d) III only e) II and III
*** What confuses me is z<3 and z<-3. Am I taking the right approach?
z ^ 2 < 9 is a quadratic inequality
z ^2 -9 < 0
(z-3) < 0 & (z+3 ) > 0 means z<3 and z > -3 --> -3 < z < 3
or
(z-3) > 0 & (z+3) <0 z> 3 or z < -3 means z is between [- infinity, 3] and [3, Infinity]
I am guessing that we ignore the second one because this graph is a parabola and we are only concerned with the points at which it cuts the x axis. Hence we ignore the second set.