f(x+y)=f(x)*f(y)-xy

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Solution for f(x+y)=f(x)*f(y)-xy equation: 


Simplifying
f(x + y) = f(x) * f(y) + -1xy
(x * f + y * f) = f(x) * f(y) + -1xy
(fx + fy) = f(x) * f(y) + -1xy

Multiply f * x
fx + fy = fx * f * y + -1xy

Multiply fx * f
fx + fy = f2x * y + -1xy

Multiply f2x * y
fx + fy = f2xy + -1xy

Solving
fx + fy = f2xy + -1xy

Solving for variable 'f'.

Reorder the terms:
fx + fy + -1f2xy + xy = f2xy + -1f2xy + -1xy + xy

Combine like terms: f2xy + -1f2xy = 0
fx + fy + -1f2xy + xy = 0 + -1xy + xy
fx + fy + -1f2xy + xy = -1xy + xy

Combine like terms: -1xy + xy = 0
fx + fy + -1f2xy + xy = 0

The solution to this equation could not be determined.

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