I'm solving an expression like so:
Solve[u[x] == u[a] + u[b], x]
Mathematica returns
{{x->(u^(-1))[u[a]+u[b]]}}
If I now specify the function u
more precisely, via
% /. {u[x_] -> x}
what I get is
{{x->(u^(-1))[a+b]}}
i.e. Mathematica replaces the function but not its inverse. Is there any way of replacing the inverse appropriately as well?