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Question Number 3963 by 123456 last updated on 25/Dec/15

f:[0,+∞)  f(αx+β)=αf(x)+β  f(x)=?

$${f}:\left[\mathrm{0},+\infty\right) \\ $$$${f}\left(\alpha{x}+\beta\right)=\alpha{f}\left({x}\right)+\beta \\ $$$${f}\left({x}\right)=? \\ $$

Answered by prakash jain last updated on 25/Dec/15

f(x)=x

$${f}\left({x}\right)={x} \\ $$

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