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# Which of the following expressions is defined for all

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Senior Manager
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Which of the following expressions is defined for all [#permalink]

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29 Oct 2006, 10:28
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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 only

... I'm not sure what the question is asking for... This is from Kaplan.
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Manager
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29 Oct 2006, 10:43
d. III only

z, such that z^2<9 implies that z can be -2, -1, 0, 1 and 2

I and II are not defined for z=0 and z=-2 as the denominator = 0
III is defined for all the above mentioned values of z

hope i didnt screw it up somewhere....

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Senior Manager
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29 Oct 2006, 10:49
I think III is also not defined. If z=-1, denominator becomes 0.

so maybe the answer is a. none

sorry, i don't have the oa for this. another kaplan question here.
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Senior Manager
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29 Oct 2006, 10:51
Well missed that fist choice contains a Z...so anwer will be A.

Last edited by yogeshsheth on 29 Oct 2006, 22:59, edited 1 time in total.

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29 Oct 2006, 10:54
Hermione wrote:
I think III is also not defined. If z=-1, denominator becomes 0.

so maybe the answer is a. none

sorry, i don't have the oa for this. another kaplan question here.

ur right... none!

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VP
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29 Oct 2006, 20:27
none.

basically it means the denominator can't be 0 and find z.

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29 Oct 2006, 21:09
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.

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Re: PS: Unclear Question   [#permalink] 29 Oct 2006, 21:09
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