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f-N-N-f-n-m-f-n-m-f-0-k-f-n-




Question Number 2187 by 123456 last updated on 07/Nov/15
f:N→N  f(n+m)=f(n)+αm  f(0)=k  f(n)=?
$${f}:\mathbb{N}\rightarrow\mathbb{N} \\ $$$${f}\left({n}+{m}\right)={f}\left({n}\right)+\alpha{m} \\ $$$${f}\left(\mathrm{0}\right)={k} \\ $$$${f}\left({n}\right)=? \\ $$
Answered by prakash jain last updated on 07/Nov/15
f(n)=f(0+n)=f(0)+αn=k+αn
$${f}\left({n}\right)={f}\left(\mathrm{0}+{n}\right)={f}\left(\mathrm{0}\right)+\alpha{n}={k}+\alpha{n} \\ $$

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