Question

What is the value of f(1) + f(2) + f(3) + ...... f(10)? Thanks in advance for the answer.

Answer 1

See below.

Explanation:

Making `x->1/x` we have

`f(1/x)+1/x^2f(x) = 1/x^2-1 rArr x^2 f(1/x)+f(x) = 1-x^2`

so we conclude that

`f(x)+x^2f(1/x) = 0`

Showing that the functional equation only has sense for

`x^2-1=0` or for `x = pm 1`