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Question Number 57020 by 121194 last updated on 28/Mar/19

$${[f(x+1)-f\left(x\right)]}^2=4[f\left(x\right)-1]$$$$f\left(x\right)=?$$$$-------------$$$$f\left(0\right)=0$$

Commented by kaivan.ahmadi last updated on 28/Mar/19

$$theinformationisnotenough$$

Commented by kaivan.ahmadi last updated on 28/Mar/19

$$iff\left(x\right)=k=constant\Rightarrow$$$$4(f\left(x\right)-1)=0\Rightarrow f\left(x\right)=1$$$$iff\left(x\right)=ax+b\Rightarrow f(x+1)=ax+a+b\Rightarrow$$$$a^2=4(ax+b-1)\Rightarrow 4ax+4b-a^2-4=0\Rightarrow$$$$wecantdeterminea,b$$

Commented by prakash jain last updated on 29/Mar/19

$$x=0$$$$f{\left(1\right)}^2=-4\Rightarrow \mathrm{no}\mathrm{such}\mathrm{function}\mathrm{exists}$$

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