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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) = ? [#permalink] New post   10 Mar 2020, 01:45
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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
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B
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Jawad001
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Re: If f(x) = x^3 − 1/x^3, then f(x) + f(1/x) = ? [#permalink] New post   10 Mar 2020, 02:08
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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
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Re: If f(x) = x^3 − 1/x^3, then f(x) + f(1/x) = ? [#permalink] New post   10 Mar 2020, 02:15
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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
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Re: If f(x) = x^3 − 1/x^3, then f(x) + f(1/x) = ? [#permalink] New post   10 Mar 2020, 02:21
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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
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Re: If f(x) = x^3 − 1/x^3, then f(x) + f(1/x) = ? [#permalink] New post   10 Mar 2020, 03:32
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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)

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Re: If f(x) = x^3 − 1/x^3, then f(x) + f(1/x) = ? [#permalink] New post   10 Mar 2020, 03:41
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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
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Re: If f(x) = x^3 − 1/x^3, then f(x) + f(1/x) = ? [#permalink] New post   10 Mar 2020, 09:18
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Quote:
If f(x) = x^3 − 1/x^3, then f(x) + f(1/x) = ?
A. -1
B. 0
C. 1
D. 2
E. 3


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)
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Re: If f(x) = x^3 − 1/x^3, then f(x) + f(1/x) = ? [#permalink] New post   10 Mar 2020, 10:09
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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.
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Re: If f(x) = x^3 − 1/x^3, then f(x) + f(1/x) = ? [#permalink]
10 Mar 2020, 10:09
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