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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If f(x)=x^4+4x^2+7, f(x)=g(x)^2+3 and g(x) > 0, then g(x) tagged by: Max@Math Revolution ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## If f(x)=x^4+4x^2+7, f(x)=g(x)^2+3 and g(x) > 0, then g(x) ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [GMAT math practice question] If f(x)=x^4+4x^2+7, f(x)=g(x)^2+3 and g(x) > 0, then g(x)=? A. x^2+1 B. x^2+2 C. x^2+3 D. x^2-1 E. x^2-2 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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Max@Math Revolution wrote:
[GMAT math practice question]

If f(x)=x^4+4x^2+7, f(x)=g(x)^2+3 and g(x) > 0, then g(x)=?

A. x^2+1
B. x^2+2
C. x^2+3
D. x^2-1
E. x^2-2
Let x=0, with the result that f(x) = 0+0+7 = 7.
Remembering that g(x)>0 and plugging f(x)=7 into f(x)=g(x)Â˛+3, we get:
7 = g(x)Â˛+3
4 = g(x)Â˛
g(x) = 2

Since the question stem asks for the value of g(x), the correct answer must yield 2 when x=0.
Only B works:
xÂ˛+2 = 0Â˛+2 = 2

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g(x)^2 = f(x) - 3 = x^4+4x^2+7 - 3 = x^4+4x^2+4 = (x^2+2)^2
Thus, since g(x) > 0, g(x)=x^2+2.

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