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Assume the function f(x) is defined as follows: f(x) = (x [#permalink]
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Question Stats: 28% (00:44) correct 71% (00:29) wrong based on 38 sessions
Assume the function f(x) is defined as follows: $$f(x) = (x-4)^2 + \sqrt{(x+3)} + \frac{5}{x+2}$$. For Which of the following values of x is f(x) defined?

Indicate all such values.

A. -5
B. -4
C. -3
D. -2
E. -1

[Reveal] Spoiler:
C, E

Last edited by GreenlightTestPrep on 06 Jan 2019, 11:17, edited 3 times in total.
Renamed the topic and edited the question.
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Expert's post
GREHelp what is the source of the question ???
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Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests. Intern Joined: 05 Jan 2016
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Kudos [?]: 18  , given: 14

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Sorry the source of the question is Manhattan Prep Algebra Book. Intern Joined: 05 Jan 2016
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Kudos [?]: 18  , given: 14

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Can anyone provide any guidance to help answer this? Senior Manager Joined: 20 May 2014
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Re: Assume the function f(x) is defined as follows: f(x) = (x [#permalink]
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GREhelp wrote:
Assume the function f(x) is defined as follows: $$f(x) = (x-4)^2 + \sqrt{(x+3)} + \frac{5}{x+2}$$. For Which of the following values of x is f(x) defined?

Indicate all such values.

A. -5
B. -4
C. -3
D. -2
E. -1

The answer is C and E. I could only select one in the official answer choice box.

You should know two properties:

1. The square root from a negative number is not defined, thus x+3 must be more than or equal to 0: $$x+3 \geq 0$$ --> $$x \geq-3$$. Eliminate options A, and B.

2. Division by 0 is not allowed, thus x+2 cannot be 0, which means that x cannot be -2. Eliminate D.

Hope it's clear. Intern Joined: 12 Jul 2017
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Re: Assume the function f(x) is defined as follows: f(x) = (x [#permalink]
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Great, thanks Manager Joined: 02 Sep 2019
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Concentration: Finance
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Re: Assume the function f(x) is defined as follows: f(x) = (x [#permalink]
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No need any calculation here.
the question is asking what is the possible value of x?
and from the function notice that we have root and fraction.
There is no value for negative roots and dividing by zero is undefined.
we left with C and E. Re: Assume the function f(x) is defined as follows: f(x) = (x   [#permalink] 28 Jun 2020, 20:56
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