Functions not satisfying parallelogram identity with supremum norm

[JackTheLad]

Homework Statement

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

$$2 ||f||^2_{sup} + 2 ||g||^2_{sup} = ||f+g||^2_{sup} + ||f-g||^2_{sup}$$

(where $$|| \cdot ||_{sup}$$ is the supremum or infinity norm)

Homework Equations

Parallelogram identity: $$2||x||^2 + 2||y||^2 = ||x+y||^2 + ||x-y||^2$$ holds for any x,y

The Attempt at a Solution

Honestly no idea.

 

[Dick]

Just try some functions. It's really not hard to find an example that doesn't work.

 

[JackTheLad]

For posterity, two functions which fit nicely are
f(x) = x
g(x) = x-1


(I had tried lots of functions but they worked; not very helpful response)