Continuity and pointwise operations of functions

Reference no: EM13123263

Let f:R->R be a function that satisfies f(x+y) = f(x)+f(y) for all x,y in R.

Suppose that f is continuous on R and that f(1)=k. Prove that f(x)=kx for all x in R.

Reference no: EM13123263

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