F(x)+f(y)=f(x*y)

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

Simplifying
F(x) + f(y) = f(x * y)

Multiply F * x
xF + f(y) = f(x * y)

Multiply f * y
xF + fy = f(x * y)

Reorder the terms:
fy + xF = f(x * y)

Multiply x * y
fy + xF = f(xy)

Multiply f * xy
fy + xF = fxy

Solving
fy + xF = fxy

Solving for variable 'f'.

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

Add '-1fxy' to each side of the equation.
fy + -1fxy + xF = fxy + -1fxy

Reorder the terms:
-1fxy + fy + xF = fxy + -1fxy

Combine like terms: fxy + -1fxy = 0
-1fxy + fy + xF = 0

Add '-1xF' to each side of the equation.
-1fxy + fy + xF + -1xF = 0 + -1xF

Combine like terms: xF + -1xF = 0
-1fxy + fy + 0 = 0 + -1xF
-1fxy + fy = 0 + -1xF
Remove the zero:
-1fxy + fy = -1xF

Combine like terms: -1xF + xF = 0
-1fxy + fy + xF = 0

The solution to this equation could not be determined.