- #1

Saitama

- 4,243

- 93

## Homework Statement

Let ## n \geq 2## be a fixed integer. ##f(x)## be a bounded function defined in ##f:(0,a) \rightarrow R## satisfying

[tex]f(x)=\frac{1}{n^2}\sum_{r=0}^{(n-1)a} f\left(\frac{x+r}{n}\right)[/tex]

then ##f(x)## =

a)-f(x)

b)2f(x)

c)f(2x)

d)nf(x)

## Homework Equations

## The Attempt at a Solution

I see no way of simplifying the summation. I need a few hints to start with.

Any help is appreciated. Thanks!