- #1

- 7

- 0

## Homework Statement

Find two functions [tex]f, g \in C[0,1][/tex] (i.e. continuous functions on [0,1]) which do not satisfy

[tex]2 ||f||^2_{sup} + 2 ||g||^2_{sup} = ||f+g||^2_{sup} + ||f-g||^2_{sup}[/tex]

(where [tex]|| \cdot ||_{sup}[/tex] is the supremum or infinity norm)

## Homework Equations

Parallelogram identity: [tex]2||x||^2 + 2||y||^2 = ||x+y||^2 + ||x-y||^2[/tex] holds for any x,y

## The Attempt at a Solution

Honestly no idea.