If f(x) = x^3 − 1/x^3, then f(x) + f(1/x) = ?

Question

Competition Mode Question

If  f(x) = x^3 − \frac{1}{x^3} , then  f(x) + f(\frac{1}{x}) = ?

A. -1
B. 0 
C. 1 
D. 2 
E. 3

Jawad001 · Answer

If f(x)= x^3- 1/x^3, then f(x)+f(1/x)=?

A. -1
B. 0
C. 1
D. 2
E. 3
Solution :
Given:
f(x)= x^3-1/x^3 and

f(1/x) = (1/x)^3- 1/(1/x)^3 = 1/x^3 - x^3

Required:
f(x)+f(1/x)= x^3-1/x^3 + 1/x^3 - x^3 = 0
Answer: B

ayushkumar22941 · Answer

we have f(x)=x^3- 1/x^3 so to get f(1/x) we replace x with 1/x which will follow to 
f(1/x)=1/x^3 - x^3
now adding the two we get f(x)+f(1/x)=0

ArunSharma12 · Answer

If  f(x)=x^3−\frac{1}{x3} , then f(x)+f(1/x)=?

f(1/x) =  \frac{1}{x^3}-x^3

f(x)+f(1/x) = 0.
Ans: B

freedom128 · Answer

f(x) = x^3 − 1/x^3
f(1/x) = 1/x^3 − x^3
f(x) + f(1/x) = 0.

FINAL ANSWER IS (B)

Posted from my mobile device

Kinshook · Answer

If f(x)=x^3−1/x^3
, then f(x)+f(1x)= x^3 - 1/x^3 + 1/x^3 - x^3 = 0

IMO B

exc4libur · Answer

f(1/x) = (1/x)^3 − 1/(1/x)^3
1/x^3-x^3
1/a-a
1-a^2/a

f(x) = x^3 − 1/x^3
a^2-1/a

f(x)+f(1/x)=a-1/a+1-a^2/a
(a^2-1+1-a^2)/a
0/a=0

Ans (B)

unraveled · Answer

If  f(x)=x^3−\frac{1}{x^3} , then  f(x)+f(\frac{1}{x}) =?

A. -1
B. 0
C. 1
D. 2
E. 3

f(x)=x^3−\frac{1}{x^3}  and
 
 f(\frac{1}{x}) = \frac{1}{x^3} − \frac{1}{1/x^3} 
 f(\frac{1}{x}) = \frac{1}{x^3} − x^3

Adding both
 f(x) + f(\frac{1}{x}) = x^3−\frac{1}{x^3} + \frac{1}{x^3} − x^3  = 0

Answer B.

bumpbot · Answer

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If f(x) = x^3 − 1/x^3, then f(x) + f(1/x) = ?

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If f(x) = x^3 − 1/x^3, then f(x) + f(1/x) = ?

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