Question: Given the function $f(x) = 4 \cdot 3^x$, find the value of $f(-1)$.
1. **State the problem:** We need to find the value of the function $f(x) = 4 \cdot 3^x$ when $x = -1$.
2. **Recall the formula:** The function is given by $$f(x) = 4 \cdot 3^x$$
3. **Substitute $x = -1$ into the function:**
$$f(-1) = 4 \cdot 3^{-1}$$
4. **Evaluate the exponent:**
Recall that $3^{-1} = \frac{1}{3}$, so
$$f(-1) = 4 \cdot \frac{1}{3}$$
5. **Multiply:**
$$f(-1) = \frac{4}{3}$$
6. **Final answer:**
The value of $f(-1)$ is $$\frac{4}{3}$$.
Among the given options, $\frac{4}{3}$ corresponds to the first choice.