To find \( f(2) \), we can use the recursive formula given in the problem:
\[ f(n) = 2 \cdot f(n-1) + 1 \]
We also know the base case:
\[ f(1) = -3 \]
Now, we can calculate \( f(2) \):
\[ f(2) = 2 \cdot f(1) + 1 \]
Substituting the value of \( f(1) \):
\[ f(2) = 2 \cdot (-3) + 1 \]
Calculating this gives:
\[ f(2) = -6 + 1 = -5 \]
Therefore, the value of \( f(2) \) is:
\[ \boxed{-5} \]