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Question
If f(x) = `x^3 - 1/x^3`, then `f(x) + f(1/x)` is equal to ______.
Options
2x3
`2 1/x^3`
0
1
Solution
If f(x) = `x^3 - 1/x^3`, then `"f"(x) + f(1/x)` is equal to 0.
Explanation:
Since f(x) = `x^3 - 1/x^3`
`f(1/x) = 1/x^3 - 1/(1/x^3)`
= `1/x^3 - x^3`
Hence, `f(x) + f(1/x) = x^3 - 1/x^3 + 1/x^3 - x^3`
= 0
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