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555-605 (Medium)|   Algebra|      
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erikvm
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If f(x) = (x + 3)^3, what is the range of the function f(x)? Updated on: 03 Mar 2015, 09:37
Originally posted by erikvm on 03 Mar 2015, 09:34.
Last edited by Bunuel on 03 Mar 2015, 09:37, edited 1 time in total.
Renamed the topic and edited the question.
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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?
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B
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If f(x) = (x + 3)^3, what is the range of the function f(x)? 03 Mar 2015, 09:45
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erikvm
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?
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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.

Answer: B.
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If f(x) = (x + 3)^3, what is the range of the function f(x)? 03 Mar 2015, 09:47
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erikvm
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.

Answer: B.
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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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If f(x) = (x + 3)^3, what is the range of the function f(x)? 03 Mar 2015, 10:01
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erikvm
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?
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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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If f(x) = (x + 3)^3, what is the range of the function f(x)? 05 Sep 2020, 23:19
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Bunuel
erikvm
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.

Answer: B.
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Bunuel: Got this correct, I've no problem with either question or solution. But does calculus, suggested by the word "range", appear in GMAT ?
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If f(x) = (x + 3)^3, what is the range of the function f(x)? 05 Sep 2020, 23:44
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Let

y =\( (x + \sqrt{3} )^4\)

=> \(\sqrt[4]{y}\) - \(\sqrt{3} \) = x

Square root can not take negative values and hence values should be '0' or more than than '0'.

Hence, Range is f(x) ≥ 0.

Answer C
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If f(x) = (x + 3)^3, what is the range of the function f(x)? 21 Jan 2025, 14:31
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