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  4. If f(x)=x3-(1/x3), then f(x)+f((1/x)) is equal to

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Q. If $f(x)=x^{3}-\frac{1}{x^{3}}$, then $f(x)+f\left(\frac{1}{x}\right)$ is equal to

Relations and Functions

Solution:

Since $f(x)=x^{3}-\frac{1}{x^{3}} $;
$ f\left(\frac{1}{x}\right)=\frac{1}{x^{3}}-\frac{1}{\frac{1}{x^{3}}}=\frac{1}{x^{3}}-x^{3}$
Hence, $f(x)+f\left(\frac{1}{x}\right)=x^{3}-\frac{1}{x^{3}}+\frac{1}{x^{3}}-x^{3}=0$