Which of the following expression is defined for all : DS Archive
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# Which of the following expression is defined for all

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Which of the following expression is defined for all [#permalink]

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26 Jan 2005, 22:04
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Which of the following expression is defined for all integers value of z , such that
z^2 < 9

1. (z+1)/z
2. (z-4) / (z^2 – 4z + 4)
3. 18 / (z^2 – 4z –5)
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26 Jan 2005, 22:21
z^2 < 9=>-3<z<3

1. (z+1)/z undefined when z=0

2. (z-4) / (z^2 â€“ 4z + 4)
z^2-4z-4=(z-2)^2 undefined when z=2

3. 18 / (z^2 â€“ 4z â€“5)
(z^2 â€“ 4z â€“5)=(z+1)(z-5) undifined when z=5 or z=-1

All in range of (-3,3). None is defined for all integers value of z.
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26 Jan 2005, 22:59
good question.

it is the same as above...................

if z^2<9 => z could be -2, -1, 1, and 2 since z is an integer.

1. (z+1)/z= infinite, if and when z = 0
2. (z-4)/(z^2 â€“ 4z + 4) = (z-4)/(z-2)^2 = infinite, if and when z=2
3. 18/(z^2 â€“ 4z â€“5) = 18/(z-5)(z+1) = infinite, if and when z=-1 and 5,

in GMAT infinite = undefined.
26 Jan 2005, 22:59
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