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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If f(x) = (x^6 + 1)/x^2 for all non-zero values of x, then what is the

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Math Expert V
Joined: 02 Sep 2009
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If f(x) = (x^6 + 1)/x^2 for all non-zero values of x, then what is the  [#permalink]

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If f(x) = (x^6 + 1)/x^2 for all non-zero values of x, then what is the value of f(x)?

(1) x < 0
(2) |x| = 16

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Joined: 05 Mar 2015
Posts: 1002
Re: If f(x) = (x^6 + 1)/x^2 for all non-zero values of x, then what is the  [#permalink]

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Bunuel wrote:
If f(x) = (x^6 + 1)/x^2 for all non-zero values of x, then what is the value of f(x)?

(1) x < 0
(2) |x| = 16

(1) if x = -1 then f(x)=2
if x=-2 then x would be anything else(No need for calculation)
insuff

(2) x= 16 , -16
as both numerator and denominator in (x^6 + 1)/x^2 are positive
Thus we get unique value for f(x)
suff

Ans B
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Re: If f(x) = (x^6 + 1)/x^2 for all non-zero values of x, then what is the  [#permalink]

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Bunuel wrote:
If f(x) = (x^6 + 1)/x^2 for all non-zero values of x, then what is the value of f(x)?

(1) x < 0
(2) |x| = 16

Given : f(x) = (x^6 + 1)/x^2 & x≠0

f(x) = ?

St 1: x < 0 Not sufficient as there are infinite values of "x"

St 2: |x| = 16

means x = 16 or - 16

As the value of f(x) will always be positive because we have even exponent, we can safely say that St 2 is sufficient for x = 16 or - 16.

(B)
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GMAT 1: 640 Q47 V31 Re: If f(x) = (x^6 + 1)/x^2 for all non-zero values of x, then what is the  [#permalink]

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In this question we get the function f(x) = (x^6 +1)/x^2 , where we have even powers for the variable x. We need to find the value of function f(x). So we need to get the value of x, and it does not matter whether it is negative or positive. Because even powers will always deliver positive result.
So, as per the staatements,
Statement 1 says x<0, but does not say any value for x. So insufficient.

Statement 2 says , lxl = 16 , which implies x could be anything +16, or -16, but in the introduction of this question we have seen that even powers always deliver positive result.. so we need only the value that is the magnitude of x irrespective of signs.
So statement 2 is sufficient. Answer B Re: If f(x) = (x^6 + 1)/x^2 for all non-zero values of x, then what is the   [#permalink] 17 Mar 2019, 20:29
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