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.

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- March 29th 2009, 05:43 AMwvlilgurlProof 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. - March 29th 2009, 06:45 AMstapel