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# Assume the function f(x) is defined as follows: f(x) = (x

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Assume the function f(x) is defined as follows: f(x) = (x [#permalink]  05 Jun 2016, 16:01
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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.
Founder
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Expert's post
GREHelp what is the source of the question ???
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Intern
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Kudos [?]: 18 [1] , given: 14

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Sorry the source of the question is Manhattan Prep Algebra Book.
Intern
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Kudos [?]: 18 [1] , given: 14

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Can anyone provide any guidance to help answer this?
Senior Manager
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Re: Assume the function f(x) is defined as follows: f(x) = (x [#permalink]  10 Jun 2016, 13:55
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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.
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Re: Assume the function f(x) is defined as follows: f(x) = (x [#permalink]  24 Jul 2017, 07:20
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Great, thanks
Manager
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Re: Assume the function f(x) is defined as follows: f(x) = (x [#permalink]  28 Jun 2020, 20:56
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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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