Hermione wrote:

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 only

... I'm not sure what the question is asking for... This is from

Kaplan.

The question asks which of the options gives a defined answer for z^2<9

If z^2<9, then -3<z<3, i.e z can be -2,-1,0, 1 and 2

For each of the options, if the denominator=0, then the term is not defined.

For z+1/z, denom z cannot be 0, which is one of the values for z

For (z-4)/ z^2-4z+4, denom z^2-4z+4 cannot be zero, which means z cant be 2, which is one of the values for z

Finally, for 18/ z^2 -4z-5, z^2 -4z-5 cannot be zero which means z cant be 5 or -1. Since -1 is one of the possible values for z, this term also cannot be defined by z.

So the answer is none.