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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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!
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