f(a+b)=f(a)+f(b)

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Solution for f(a+b)=f(a)+f(b) equation: 


Simplifying
f(a + b) = f(a) + f(b)
(a * f + b * f) = f(a) + f(b)
(af + bf) = f(a) + f(b)

Multiply f * a
af + bf = af + f(b)

Multiply f * b
af + bf = af + bf

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

Combine like terms: af + -1af = 0
0 + bf = af + -1af + bf
bf = af + -1af + bf

Combine like terms: af + -1af = 0
bf = 0 + bf
bf = bf

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

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

Combine like terms: bf + -1bf = 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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