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Retired Moderator

Joined: **07 Jun 2014 **

Posts: **4805**

WE:**Business Development (Energy and Utilities)**

If g(x) = , for which of the following x values is g(x) unde
[#permalink]
30 Jul 2018, 10:19

Expert Reply

2

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Question Stats:

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. \(\frac{9}{4}\)

_________________

Indicate all such values of x.

A. \(\frac{-9}{4}\)

B. \(–2\)

C. \(0\)

D. \(1\)

E. \(2\)

F. \(\frac{9}{4}\)

_________________

Sandy

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Re: If g(x) = , for which of the following x values is g(x) unde
[#permalink]
03 Aug 2018, 12:27

1

Expert Reply

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. \(\frac{9}{4}\)

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.

Answer: B, D

Cheers,

Brent

_________________

Retired Moderator

Joined: **07 Jun 2014 **

Posts: **4805**

WE:**Business Development (Energy and Utilities)**

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

1

Expert Reply

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

If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

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.

_________________

If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Re: If g(x) = , for which of the following x values is g(x) unde
[#permalink]
06 Sep 2021, 20:49

i have a doubt i tried solving this questions by plugging in the option values and i got -2,1 i wanted to know why 0 isnt also selected as an answer option cause 0 divided by 0 is also undefined

Re: If g(x) = , for which of the following x values is g(x) unde
[#permalink]
06 Sep 2021, 23:25

2

The denominator is \((3x-3)(x+2)\), so when you put \(x = 0\), it will be \(-6\) but not \(0\).

_________________

saad wrote:

i have a doubt i tried solving this questions by plugging in the option values and i got -2,1 i wanted to know why 0 isnt also selected as an answer option cause 0 divided by 0 is also undefined

_________________

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