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GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 105

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If g(x) = , for which of the following x values is g(x) unde [#permalink]
Expert's post 00:00

Question Stats: 80% (00:44) correct 20% (02:11) wrong based on 10 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: 1543
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Kudos [?]: 1468 , given: 8

Re: If g(x) = , for which of the following x values is g(x) unde [#permalink]
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 Sign up for our free GRE Question of the Day emails

GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1783 , given: 397

Re: If g(x) = , for which of the following x values is g(x) unde [#permalink]
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.
_________________

Sandy
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Try our free Online GRE Test 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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