Thread: Proof Question 3

Suppose that the function f : R -> R has the property that F(u+v) = f(u)+f(v) for all u and v.

Define m = f(1). Prove that f(x)=mx for all rational numbers x and use this to prove that if f : R->R is continuous then f(x)=mx for all x.

Originally Posted by wvlilgurl

Suppose that the function f : R -> R has the property that F(u+v) = f(u)+f(v) for all u and v.

How is "F(x)" (in contrast to "f(x)") defined?

What are your thoughts and efforts so far? Please be complete. Thank you!