Find \( f(x)+f(1/x) \)
Question:
If
\[ f(x)=x^3-\frac1{x^3} \]
then
\[ f(x)+f\left(\frac1x\right) \]
is equal to
(a) \(2x^3\)
(b) \(\frac2{x^3}\)
(c) \(0\)
(d) \(1\)
Solution:
\[ f\left(\frac1x\right) = \left(\frac1x\right)^3 – \frac1{\left(\frac1x\right)^3} \]
\[ = \frac1{x^3}-x^3 \]
Therefore,
\[ f(x)+f\left(\frac1x\right) = \left(x^3-\frac1{x^3}\right) + \left(\frac1{x^3}-x^3\right) \]
\[ =0 \]
Hence,
\[ \boxed{\text{Correct Answer: (c)}} \]