Determine whether the statement is true or false. If f is a function, then f (a + b) = f (a) + f (b).
A) False
B) True

Question

Quizplus · Accepted Answer

The statement is known as the Cauchy functional equation and not all functions satisfy it. For example, any function of the form f(x) = cx (where c is a constant) does satisfy the equation, but some non-linear functions like f(x) = x^2 do not satisfy the equation. Therefore, the statement is false in general.

Determine Whether the Statement Is True or False