Question

\begin{cases}
f(1)=-3
\\\\
f(n)=2 \cdot f(n-1) + 1
\end{cases}
f(2)=

Answer 1

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:

\[
\boxed{-5}
\]