Răspuns:
A(1;1)=> f(1)=a+b=1
B(-1;3)=> f(-1)=-a+b=3
Adunam relatiile obținute.
a+b-a+b=4
2b=4=> b=2
a+2=1=>a=-1
=> f(x)=-x+2
[tex]f:\mathbb{R}\to \mathbb{R},f(x) = ax+b \\ \\ A(1;1) \in Gf \Rightarrow f(1) = 1 \Rightarrow a\cdot 1+b = 1 \Rightarrow a+b = 1 \\ B(-1;3)\in Gf \Rightarrow f(-1) = 3 \Rightarrow a\cdot (-1)+b = 3 \Rightarrow -a+b = 3\\ \\ (\text{Adunam cele 2 ecuatii:) }\\ \\ a-a+b+b = 1+3 \Rightarrow 2b = 4 \Rightarrow b = 2 \\ a+2 = 1 \Rightarrow a = -1 \\ \\ \Rightarrow \boxed{f(x) = -x+2}[/tex]
