The function $f(x)$ is defined piecewise with two different expressions depending on the interval of $x$. The function appears to have an issue with formatting, so let's clarify it based on standard piecewise notation. It seems like the function should be written as:

\begin{cases} 3x + 17 & \text{if } -3 < x < 2 \\ x - 4 & \text{if } 3 < x < 6 \end{cases}$$ To find the value of $$f(x)$$ at $$x = -2$$, we need to determine which interval this value of $$x$$ belongs to. ### Step 1: Identify the appropriate interval for $$x = -2$$ Since $$-2$$ falls within the interval $$-3 < x < 2$$, we use the first expression: $$f(x) = 3x + 17.$$ ### Step 2: Substitute $$x = -2$$ into the expression $$f(-2) = 3(-2) + 17.$$ Calculating this gives: $$f(-2) = -6 + 17 = 11.$$ It appears none of the provided answer choices match the correct calculation, suggesting there might be an error in the available options. Would you like to double-check the intervals or clarify anything further? Here are some related questions to deepen understanding: 1. How do you handle piecewise functions when $$x$$ is at the boundary of intervals? 2. What would be the value of $$f(x)$$ at $$x = 0$$? 3. How does the function behave between intervals? 4. What would be the value of $$f(x)$$ if $$x = 4$$? 5. Could boundary conditions alter the output of a piecewise function? **Tip:** Always confirm the function’s interval before substituting values, especially with piecewise-defined functions.