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# If f(x) = (x + 3)^3, what is the range of the function f(x)?

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Joined: 26 Feb 2015
Posts: 123
If f(x) = (x + 3)^3, what is the range of the function f(x)? [#permalink]

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03 Mar 2015, 08:34
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70% (02:14) correct 30% (01:11) wrong based on 87 sessions

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If $$f(x) =(x + \sqrt{3})^4$$, what is the range of the function f(x)?

(A)$$\sqrt{3} < f(x) < 4$$

(B) f(x) >= 0

(C) f(x) < 0

(D) $$f(x) \neq{0}$$

Can someone please provide an explaination to this one?
[Reveal] Spoiler: OA

Last edited by Bunuel on 03 Mar 2015, 08:37, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 43853
Re: If f(x) = (x + 3)^3, what is the range of the function f(x)? [#permalink]

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03 Mar 2015, 08:45
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erikvm wrote:
If $$f(x) =(x + \sqrt{3})^4$$, what is the range of the function f(x)?

(A)$$\sqrt{3} < f(x) < 4$$

(B) f(x) >= 0

(C) f(x) < 0

(D) $$f(x) \neq{0}$$

Can someone please provide an explaination to this one?

f(x) equals to the even (4th) power of some number, thus it cannot be less than 0.
If $$x = - \sqrt{3}$$, then f(x) = 0.

So, f(x) >= 0.

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Math Expert
Joined: 02 Sep 2009
Posts: 43853
Re: If f(x) = (x + 3)^3, what is the range of the function f(x)? [#permalink]

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03 Mar 2015, 08:47
Bunuel wrote:
erikvm wrote:
If $$f(x) =(x + \sqrt{3})^4$$, what is the range of the function f(x)?

(A)$$\sqrt{3} < f(x) < 4$$

(B) f(x) >= 0

(C) f(x) < 0

(D) $$f(x) \neq{0}$$

Can someone please provide an explaination to this one?

f(x) equals to the even (4th) power of some number, thus it cannot be less than 0.
If $$x = - \sqrt{3}$$, then f(x) = 0.

So, f(x) >= 0.

Check other function questions in our Special Questions Directory:

Operations/functions defining algebraic/arithmetic expressions
Symbols Representing Arithmetic Operation
Rounding Functions
Various Functions
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Joined: 07 Aug 2011
Posts: 578
GMAT 1: 630 Q49 V27
If f(x) = (x + 3)^3, what is the range of the function f(x)? [#permalink]

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03 Mar 2015, 09:01
1
KUDOS
erikvm wrote:
If $$f(x) =(x + \sqrt{3})^4$$, what is the range of the function f(x)?

(A)$$\sqrt{3} < f(x) < 4$$

(B) f(x) >= 0

(C) f(x) < 0

(D) $$f(x) \neq{0}$$

Can someone please provide an explaination to this one?

MIN (F(X)) is when X= - $$\sqrt{3}$$ So MIN(F(X)) = 0
MAX(F(X)) --> no boundary
(B) f(x) >= 0 is the answer
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Posts: 13815
Re: If f(x) = (x + 3)^3, what is the range of the function f(x)? [#permalink]

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05 Oct 2017, 10:34
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If f(x) = (x + 3)^3, what is the range of the function f(x)?   [#permalink] 05 Oct 2017, 10:34
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