[Edited for clarification after comment]
Suppose that the function f is defined as the linear combination of several translated/reflected functions starting from the primitive f0[x,y,z]
f[x_, y_, z_] := f0[x,y,z-z1]+f0[x,y,z-z3]+f0[x,y,z-3z2+z1]
wherein z1,z2,z3,... are real positive numbers. The actual composition of f is not known, but it follows the above pattern.
I would like then to construct the function g obtained from f by considering the negative value of the third argument. The required output in this example would be
g[x_, y_, z_] := f0[x,y,-(z-z1)]+f0[x,y,-(z-z3)]+f0[x,y,-(z-3z2+z1)]
I cannot simply do
g[x_, y_, z_] := f[x, y, -z]
since this would yield
f0[x, y, -z - z1] + f0[x, y, -z + z1 - 3 z2] + f0[x, y, -z - z3]
How would is that possible to find and isolate in general the third argument of f0 so that the proper substitution can be applied? Or what would be the cleanest way of define the functions f and g?
Thank you all very much for sharing your knowledge and advice.