Resposta :
Olá, Sillas.
[tex]f(x + 1) = 2f(x) + f(1) \Rightarrow \\\\ f(2+1)=2f(2)+f(1) \Rightarrow \\\\ f(3)=2f(2)+f(1) \Rightarrow \\\\ 6=2f(2)+f(1)\text{ (i)} \\\\ \text{Por outro lado:} \\\\ f(1+1)=2f(1)+f(1) \Rightarrow \\\\ f(2)=3f(1)\text{ (ii)} \\\\ \text{Substituindo (ii) em (i):}[/tex]
[tex]6=2\cdot3f(1)+f(1) \Rightarrow \\\\ 6=7f(1) \Rightarrow \\\\ \boxed{f(1)=\frac67}[/tex]
[tex]f(x + 1) = 2f(x) + f(1) \Rightarrow \\\\ f(2+1)=2f(2)+f(1) \Rightarrow \\\\ f(3)=2f(2)+f(1) \Rightarrow \\\\ 6=2f(2)+f(1)\text{ (i)} \\\\ \text{Por outro lado:} \\\\ f(1+1)=2f(1)+f(1) \Rightarrow \\\\ f(2)=3f(1)\text{ (ii)} \\\\ \text{Substituindo (ii) em (i):}[/tex]
[tex]6=2\cdot3f(1)+f(1) \Rightarrow \\\\ 6=7f(1) \Rightarrow \\\\ \boxed{f(1)=\frac67}[/tex]