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

[Max@Math Revolution]

[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

[Brent@GMATPrepNow]

[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

[Max@Math Revolution]

=>


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