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Question Number 652 by 123456 last updated on 19/Feb/15

$$iff:\mathbb{R}\to \mathbb{R}iscontinuousand$$$$f(x+y)=f\left(x\right)+y$$$$1.findf\left(x\right)$$$$2.proofordisproofthat{f}^{\prime }\left(x\right)=1$$$$3.iff\left(0\right)=0proofordisproofthatf\left(x\right)=x$$

Answered by prakash jain last updated on 19/Feb/15

$$f(x+y)=f\left(x\right)+y$$$$f\left(y\right)=f\left(0\right)+y$$$$\mathrm{or}f\left(x\right)=x+f\left(0\right).....\left(1\right)$$$$f{}^{\prime }\left(x\right)=1$$$$f\left(0\right)=0\Rightarrow f\left(x\right)=x$$$$$$

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