Mathematics Homework Solutions
Problem
#8953

Continuous Functions

Suppose that f(x) satisfies the functional equation

     f(x + y) = f(x) + f(y)

for all x,y in R (the real numbers).  Prove that if f(x) is continuous that f(x) = cx where c is a constant.  What can you say about f(x) if it is allowed to be discontinuous?


Solution Summary

The notion of discontinuity in relation to a given function is investigated.

Solution
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Badri Padhukasahasram, PhD (IP) - 4.6/5
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