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

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by Max@Math Revolution » Mon May 20, 2019 12:52 am

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[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
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by GMATGuruNY » Mon May 20, 2019 2:26 am
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)²+3, we get:
7 = g(x)²+3
4 = g(x)²
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:
x²+2 = 0²+2 = 2

The correct answer is B.
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by Max@Math Revolution » Tue May 21, 2019 11:38 pm
=>

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.

Therefore, B is the answer.
Answer: B
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