f(x)*f(y)=g(x-y)

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


Simplifying
f(x) * f(y) = g(x + -1y)

Multiply f * x
fx * f * y = g(x + -1y)

Multiply fx * f
f2x * y = g(x + -1y)

Multiply f2x * y
f2xy = g(x + -1y)
f2xy = (x * g + -1y * g)
f2xy = (gx + -1gy)

Solving
f2xy = gx + -1gy

Solving for variable 'f'.

Move all terms containing f to the left, all other terms to the right.

Divide each side by 'xy'.
f2 = gy-1 + -1gx-1

Simplifying
f2 = gy-1 + -1gx-1

Reorder the terms:
f2 = -1gx-1 + gy-1

Reorder the terms:
f2 + gx-1 + -1gy-1 = -1gx-1 + gx-1 + gy-1 + -1gy-1

Combine like terms: -1gx-1 + gx-1 = 0
f2 + gx-1 + -1gy-1 = 0 + gy-1 + -1gy-1
f2 + gx-1 + -1gy-1 = gy-1 + -1gy-1

Combine like terms: gy-1 + -1gy-1 = 0
f2 + gx-1 + -1gy-1 = 0

The solution to this equation could not be determined.

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