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Question Number 82570 by jagoll last updated on 22/Feb/20

$$iff\left(x\right)=f(x+1)-x$$$$findf\left(x\right)$$

Commented by Tony Lin last updated on 22/Feb/20

$$f(x+1)-f\left(x\right)=x$$$$\Rightarrow f\left(0\right)=f\left(1\right)$$$$\Rightarrow f\left(x\right)=kx(x-1)+c$$$$k[(x+1)x-x(x-1)]=x$$$$k=\frac{1}{2}$$$$\Rightarrow f\left(x\right)=\frac{1}{2}x(x-1)+c$$

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