If f(x) = (x + âˆš3)^4, what is the range of the function f(

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vinni.k: Master | Next Rank: 500 Posts; Posts: 421; Joined: Sun Apr 17, 2011 4:27 amFollowed by: 2 members; Location: India; Thanked: 6 times; GMAT Score:620

by vinni.k » Wed Dec 05, 2012 2:07 am

Source:- MGMAT equations

If f(x) = (x + âˆš3)^4, what is the range of the function f(x) ?

A. âˆš3 < f(x) < 4
B. f(x) >= 0
C. f(x) < 0
D. f(x) not equal to 0

Answer is B

Why A cannot be the answer ?

Thanks & Regards
Vinni

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Source: Beat The GMAT — Problem Solving | Wed Dec 05, 2012 2:07 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Dec 05, 2012 2:35 am

vinni.k wrote:Source:- MGMAT equations

If f(x) = (x + âˆš3)^4, what is the range of the function f(x) ?

A. âˆš3 < f(x) < 4
B. f(x) >= 0
C. f(x) < 0
D. f(x) not equal to 0

Answer is B

Why A cannot be the answer ?

Thanks & Regards
Vinni

The RANGE is composed of ALL possible values of f(x).
If x = -âˆš3, then f(-âˆš3) = (-âˆš3 + âˆš3)â�´ = 0.
Since the correct answer must include 0 within its range, eliminate A, C and D.

The correct answer is B.

(x + âˆš3)â�´ can be equal to any NONNEGATIVE value.
Thus, the range of f(x) = (x + âˆš3)â�´ is any value greater than or equal to 0.

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vinni.k: Master | Next Rank: 500 Posts; Posts: 421; Joined: Sun Apr 17, 2011 4:27 amFollowed by: 2 members; Location: India; Thanked: 6 times; GMAT Score:620

by vinni.k » Wed Dec 05, 2012 4:28 am

GMATGuruNY wrote: The RANGE is composed of ALL possible values of f(x).
If x = -âˆš3, then f(-âˆš3) = (-âˆš3 + âˆš3)â�´ = 0.
Since the correct answer must include 0 within its range, eliminate A, C and D.

The correct answer is B.

(x + âˆš3)â�´ can be equal to any NONNEGATIVE value.
Thus, the range of f(x) = (x + âˆš3)â�´ is any value greater than or equal to 0.

Thanks Mitch. As always you are the best. Making things easier to understand.

Regards
Vinni

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