[tex]\displaystyle\\f_a(x)=(a+1)x-a+2\\\\a)~~\text{Rezolvam ecuatia:}\\\\f_a(0)=1\\\\(a+1)\cdot0-a+2=1\\\\-a+2=1\\\\-a=1-2\\\\-a=-1~\Big|\cdot(-1)\\\\\boxed{\bf a=1}\\\\b)~~\text{Aratam ca:}\\f_a(1)=3~\text{oricare ar fi }a\in\mathbb R\\\\f_a(1)=(a+1)\cdot1-a+2=a+1-a+2=1+2=3\\\\\implies~\boxed{B(1,~3)~\in G(f_a)~~ \forall~~a\in\mathbb R}[/tex]
[tex]\displaystyle\\c)\\\\\text{Graficul functiei este paralel cu Ox daca functia este constanta.}\\\\\implies~\text{Coeficientul lui x este egal cu 0.}\\\\f_a(x)=(a+1)x-a+2\\\\a+1=0\\\\\boxed{\bf a=-1}\\\\f_{-1}(x)=(-1+1)x-(-1)+2\\\\f_{-1}(x)=0x+1+2\\\\f_{-1}(x)=3~~\text{(functie constanta)}[/tex]
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