1. Tardigrade
  2. Question
  3. Mathematics
  4. If f(x) = x3 - (1/x3), then f(x) + f((1/x)) is equal

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

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