A proof of mathematical function Let an implicit function satisfy f (x, y) = f (y, x) = K (k is a constant) It is proved that the explicit function y = f (x) determined by F (x, y) = k must satisfy f (x) = F-1 (x)

y=f(x) x=f-1(x)
F(x,f(x))=F(f(x),x)=F(f(f-1()x),f-1(x))=F(x,f-1(x))
f(x)=f-1(x)

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