x=a+b,f(a)=a,f(b)=-b.
f(x)=a-b.

a=(x+f(x))/2,b=(x-f(x))/2.
x=a+b,f(a)=a,f(b)=-b.

a+b=c+d,f(a)=a,f(b)=-b,f(c)=c,f(d)=-d.
a-b=c-d.
a=c,b=d.