Assume we have 2 peaked positive functions
f[x_] := Exp[-(x + 3)^2] g[x_] := 1/2 Exp[-(x - 3)^2/4]
that look like
Would it be possible to numerically find a morphed function such as
h[x_] := 2/3 Exp[-4 (x)^2/9]
(depicted below as orange)? Notice, linear interpolation (blue) fails miserably as the graph below shows.
Please, assume some blackbox functions. It is clear that the problem is very simple when an analytical expression is given.
Because of the fuzzy formulation, the solution cannot be unique.