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If g(x) = , for which of the following x values is g(x) unde

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Retired Moderator
Joined: 07 Jun 2014
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GRE 1: Q167 V156
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If g(x) = , for which of the following x values is g(x) unde [#permalink]  30 Jul 2018, 10:19
Expert's post
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Question Stats:

72% (00:33) correct 27% (00:54) wrong based on 37 sessions
If $$g(x) = \frac{x^2(4x+9)}{(3x-3)(x+2)}$$, for which of the following x values is g(x) undefined?

Indicate all such values of x.

A. $$\frac{-9}{4}$$
B. $$–2$$
C. $$0$$
D. $$1$$
E. $$2$$
F. $$\frac{9}{4}$$
[Reveal] Spoiler: OA

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Sandy
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GRE Instructor
Joined: 10 Apr 2015
Posts: 3826
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Kudos [?]: 4470 [1] , given: 69

Re: If g(x) = , for which of the following x values is g(x) unde [#permalink]  03 Aug 2018, 12:27
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KUDOS
Expert's post
sandy wrote:
If $$g(x) = \frac{x^2(4x+9)}{(3x-3)(x+2)}$$, for which of the following x values is g(x) undefined?

Indicate all such values of x.

A. $$\frac{-9}{4}$$
B. $$–2$$
C. $$0$$
D. $$1$$
E. $$2$$
F. $$\frac{9}{4}$$

A rational expression (aka fraction) is considered undefined when the denominator is zero

In this question the denominator is (3x-3)(x+2)
So, the denominator will equal zero when (3x-3) = 0 or (x+2) = 0

Let's examine each case separately.
If (3x-3) = 0, the x = 1
If (x+2) = 0, the x = -2

So, when x = 1, the fraction is undefined.
Likewise, when x = -2, the fraction is undefined.

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
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Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 171

Kudos [?]: 2914 [0], given: 394

Re: If g(x) = , for which of the following x values is g(x) unde [#permalink]  11 Aug 2018, 16:38
Expert's post
Explanation

The term “undefined” refers to the circumstance when the solution is not a real number —for example, division by 0 is considered “undefined.” There aren’t many circumstances that result in an undefined answer.

Essentially, the GRE considers two main cases: the square root of a negative integer and division by 0. There are no square roots in this problem, but it’s possible that 0 could end
up on the denominator of the fraction. Set each of the terms in the denominator equal to 0:
$$3x - 3 = 0$$
$$3x = 3$$
$$x = 1$$
$$x + 2 = 0$$
$$x = -2$$

Thus, if x = 1 or x = –2, then the denominator would be 0, making g(x) undefined. All other values are acceptable.
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Re: If g(x) = , for which of the following x values is g(x) unde   [#permalink] 11 Aug 2018, 16:38
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