We have that
[tex]g(n)=g(n-1)+2[/tex]
then
[tex]\begin{gathered} g(2)=g(1)+2 \\ g(3)=g(2)+2=g(1)+2+2=g(1)+4 \\ g(4)=g(3)+2=g(1)+4+2=g(1)+6 \\ \ldots \end{gathered}[/tex]
so, we see that a closed-form is
[tex]\begin{gathered} f(x)\text{ = g(1)+2(x-1)} \\ f(x)=5+2x-2 \\ f(x)=2x+3 \end{gathered}[/tex]
Then, the answer is the second one
