MathGroup Archive 2004

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Intra functional relations


This may be almost frivolous: If f[x_]+f[y_]=f[x*y],then,
can Mathematica prove or solve f[x_]= C Log[x],( C arbitrary constant)
?
Also, if g[x_+y_]=g[x]*Sqrt[1- g[y]^2] + Sqrt[1- g[x]^2]*g[y],then,
can it be proved that g[x_]=Sin[x]? Can the function capabilities of
Mathematica in some way be put to use here?  Regards.


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