f(x+y)=f(x)+f(y)

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


Simplifying
f(x + y) = f(x) + f(y)
(x * f + y * f) = f(x) + f(y)
(fx + fy) = f(x) + f(y)

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

Multiply f * y
fx + fy = fx + fy

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

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

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

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

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

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

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

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