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Mathematics Question on Relations and functions

If f(x)=x3−1x3f(x) = x^3 - \frac{1}{x^3}, then f(x)+f(1x)f(x) + f(\frac{1}{x}) is equal

A

2x32 x^3

B

21x32 \frac{1}{x^3}

C

0

D

1

Answer

0

Explanation

Solution

Since f(x)=x3−1x3f(x) = x^3 - \frac{1}{x^3} f(1x)=1x3−11x3=1x3−x3f\left(\frac{1}{x}\right) = \frac{1}{x^{3}} - \frac{1}{\frac{1}{x^{3}}} = \frac{1}{x^{3}} - x^{3} Hence, f(x)+f(1x)=x3−1x3+1x3−x3=0f\left(x\right) + f\left(\frac{1}{x}\right) = x^{3} - \frac{1}{x^{3} }+ \frac{1}{x^{3}} - x^{3} = 0