Thursday, February 1, 2018

analysis - If f(x+y)=f(x)+f(y) showing that f(cx)=cf(x) holds for rational c



For f:RnRm, if f(x+y)=f(x)+f(y) for then for rational c, how would you show that f(cx)=cf(x) holds?



I tried that for c=ab, a,bZ clearly
f(abx)=f(xb++xb)=af(xb)


but I can't seem to finish it, any help?


Answer



Try computing bf(x/b).


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