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

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


Simplifying
f(x) + f(y) + -1f(x + y) = xy

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

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

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

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

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

Solving
0 = xy

Solving for variable 'x'.

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

Add '-1xy' to each side of the equation.
0 + -1xy = xy + -1xy
Remove the zero:
-1xy = xy + -1xy

Combine like terms: xy + -1xy = 0
-1xy = 0

Divide each side by '-1'.
xy = 0

Simplifying
xy = 0

The solution to this equation could not be determined.

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