Function Proof

[dobobo]

Find mistake in the logic :

Someone created dual function f: R -> R that creates symmetry
(For that to be symmetry f(x) +f(1-x) = 1 for all x, but dual functions usually f(x) +f(1-x) \< 1, x /= 1/2)

h : R -> R prove that
h(x): ( f(x) if x=/ x1 )
( 1-f(1-x1) other cases)

 

[Dr.Peterson]

Find mistake in the logic :

Someone created dual function f: R -> R that creates symmetry
(For that to be symmetry f(x) +f(1-x) = 1 for all x, but dual functions usually f(x) +f(1-x) \< 1, x /= 1/2)

h : R -> R prove that
h(x): ( f(x) if x=/ x1 )
( 1-f(1-x1) other cases)

I think we need some context. What do you mean by "dual function" in your context, and what kind of symmetry do you have in mind?

And why do you say there is a mistake in logic when you either haven't defined h, or haven'tsaid what is to be proved (depending on whether I take the last bit as a theorem or a definition of h), much less shown a proof?