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Definition of an exponential function

• To: mathgroup at smc.vnet.net
• Subject: [mg31665] Definition of an exponential function
• From: "PSi" <psino at tee.gr>
• Date: Fri, 23 Nov 2001 05:46:52 -0500 (EST)
• Organization: National Technical University of Athens, Greece
• Sender: owner-wri-mathgroup at wolfram.com

I want to define a function with the properties of Exp.
The definition
f[x_+y_]:=f[x]f[y]
f[m_  x_]:=f[x]^m
f[0]=1
gives
f[x]^2 f[-x]^2=1
but
f[x]^m f[-x]^m=(1/f[x])^m (f[x])^m.
Is there a way in Mathematica 4.1 to obtain f[x]^m f[-x]^m=1?