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When f(x)=x^3+1/x3, which of the following is equal to f(-1/

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by Max@Math Revolution » Sun Mar 24, 2019 11:15 pm

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A

B

C

D

E

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[GMAT math practice question]

When f(x)=x^3+1/x3, which of the following is equal to f(-1/x)?

A. f(x)
B. -f(x)
C. 1/f(x)
D. 1-f(x)
E. (f(x))^3
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by Brent@GMATPrepNow » Mon Mar 25, 2019 5:43 am
Max@Math Revolution wrote:[GMAT math practice question]

When f(x)=x³ + 1/x³, which of the following is equal to f(-1/x)?

A. f(x)
B. -f(x)
C. 1/f(x)
D. 1-f(x)
E. (f(x))^3
GIVEN: f(x)=x³ + 1/x³
So, f(-1/x) = (-1/x)³ + 1/(-1/x)³
= -1/x³ + 1/(-1/x³)
= -1/x³ - x³
= -(1/x³ + x³)
= -(x³ + 1/x³)
= -f(x)

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Tue Mar 26, 2019 11:56 pm
=>


f(-1/x) = (-1/x)^3 + 1/{1/(-1/x)^3} = -1/x^3 - x^3 = -(x^3+1/x^3) = -f(x).

Therefore, B is the answer.
Answer: B
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