If f(x) = x3 - \(\frac{1}{x^3}\), then show that f(x) + f(\(\frac{1}{

1.	If f(x) = x3 - \(\frac{1}{x^3}\), then show that f(x) + f(\(\frac{1}{x}\)) = 0
Answer» f(x) = x³ - \(\frac{1}{x^3}\) ... (1) f(\(\frac{1}{x}\)) = (\(\frac{1}{x}\))³- \(\frac{1}{(\frac{1}{x})^3}\) = \(\frac{1}{x^3}\) - x³ ... (2) (1) + (2) gives f(x) + f(\(\frac{1}{x}\)) = x³- \(\frac{1}{x^3}+\frac{1}{x^3}-x^3\) = 0 Hence Proved.

If f(x) = x3 - \(\frac{1}{x^3}\), then show that f(x) + f(\(\frac{1}{x}\)) = 0

Answer»

f(x) = x³ - \(\frac{1}{x^3}\) ... (1)

f(\(\frac{1}{x}\)) = (\(\frac{1}{x}\))³- \(\frac{1}{(\frac{1}{x})^3}\) = \(\frac{1}{x^3}\) - x³ ... (2)

(1) + (2) gives f(x) + f(\(\frac{1}{x}\))

= x³- \(\frac{1}{x^3}+\frac{1}{x^3}-x^3\) = 0

Hence Proved.