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f(x*1) = f(x) + f(1)

f(1)=0

f(1) = f(x * 1/x) = f(x) + f(1/x)

f(x) = -f(1/x)

f(x+epsilon)-f(x)

=

f(x+epsilon)+f(1/x)

=

f((x+epsilon)/x)

=

f(1+epsilon/x)

If we assume that f is analytic:

f'(1)=lim(epsilon->0:f(1+e

f'(x)=

lim(epsilon->0:(f(x+epsilo

=

lim(epsilon->0:f(1+epsilon

=

lim(epsilon->0:( f(1)+(epsilon/x)*f'(1))/ep

=

f'(1)/x

so f(x) = integral(1..x:f'(1)/x)