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

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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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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

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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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New post 07 Mar 2018, 10:03
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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Re: If f(x) = (x^6 + 1)/x^2 for all non-zero values of x, then what is the   [#permalink] 07 Mar 2018, 10:03
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