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]