We have the following:
We can see that in step 0 there are 3, in step 1 there are 4, in step 2 there are 7 and in step 3 there are 12.
Therefore we can discard the first and the last option, which when n is equal to 0, it does not correspond to 3.
[tex]\begin{gathered} f(n)=n+3 \\ f(1)=1+3=4 \\ f(2)=2+3=5 \\ \text{therefore, it is not option 2} \\ f(n)=n^2+3 \\ f(0)=0^2+3=3 \\ f(1)=1^2+3=4 \\ f(2)=2^2+3=7 \\ f(3)=3^2+3=12 \end{gathered}[/tex]
Which means that the correct option is the third
[tex]f(n)=n^2+3[/tex]
