[tex]f(\text{x}) = a\text{x}+3\\ \\ P\Big(\dfrac{1}{a+1},5\Big) \in G_f \Rightarrow f\Big(\dfrac{1}{a+1}\Big) = 5 \Rightarrow \\ \\ \Rightarrow a\cdot \dfrac{1}{a+1}+3 = 5 \Big|\cdot (a+1) \Rightarrow a+3(a+1) = 5(a+1) \Rightarrow \\ \\ \Rightarrow a = 5(a+1)-3(a+1) \Rightarrow a = 2(a+1) \Rightarrow a = 2a+2 \Rightarrow \\ \\ \Rightarrow \boxed{a = -2}[/tex]
