Question

If f : R \ {0} → R is defined by f(x) = $x^{3} - \frac{1}{x^{3}}$ then show that f(x) + f (1/x) = 0.

Answer 1

Answer:

See the attachment for detailed solution

Step-by-step explanation:

In the attachment I have answered this problem.

I hope this answer helps you

Answer 2

Answer:

f(x) + f(1/x) = 0

Step-by-step explanation:

Given: f(x) = x³ - (1/x³)

                = (x⁶ - 1)/x³.

f(1/x) = (1/x)³ - (1)/(1/x)³

        = 1/x³ - x³

        = (1 - x⁶)/x³.

LHS:

f(x) + f(1/x)

= (x⁶ - 1)/x³ + (1 - x⁶)/x³

= (x⁶ - 1 + x - x⁶)/x³

= 0.

= RHS

Hope it helps!