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Math Help - Proof Question 3

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by wvlilgurl View Post
    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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