Question

Please solve this question

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Answer 1

Here is your answer :

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

Now, we have to find ;

$f(x) + f( \frac{1}{x} ) \\ \\ \implies x {}^{3} - \frac{1}{x {}^{3} } + \frac{1}{x {}^{3} } - x {}^{3} \\ \\ \implies 0$

Hence Proved.

Answer 2

hope it helps.................