For f:Rn→Rm, 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,b∈Z clearly
f(abx)=f(xb+⋯+xb)=af(xb)
but I can't seem to finish it, any help?
Answer
Try computing bf(x/b).
For f:Rn→Rm, 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,b∈Z clearly
f(abx)=f(xb+⋯+xb)=af(xb)
Answer
Try computing bf(x/b).
I have injection f:A→B and I want to get bijection. Can I just resting codomain to f(A)? I know that every function i...
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