Question: Given the function: $$f(x) = \begin{cases} -3x^2 + 7 & x < -1 \\ 6x^2 - 2 & -1 \leq x \leq 7 \\ 6 & x > 7 \end{cases}$$
Calculate $$f(5)$$
1. **State the problem:** We need to find the value of the piecewise function $$f(x)$$ at $$x=5$$.
2. **Identify the correct piece:** Since $$5$$ satisfies $$-1 \leq 5 \leq 7$$, we use the middle piece of the function:
$$f(x) = 6x^2 - 2$$
3. **Substitute $$x=5$$ into the formula:**
$$f(5) = 6(5)^2 - 2$$
4. **Calculate the square:**
$$f(5) = 6 \times 25 - 2$$
5. **Multiply:**
$$f(5) = 150 - 2$$
6. **Subtract:**
$$f(5) = 148$$
7. **Final answer:**
$$\boxed{148}$$
So, the correct choice is E: $$f(5) = 148$$.