Math Problem Statement
The function \( f(x) \) is defined piecewise as follows:
\[
f(x) = \begin{cases}
3x + 1 & \text{for } x \neq -2 \\
2 & \text{for } x = -2
\end{cases}
\]
Find \( f(-2) \).
Solution
The function is defined piecewise as follows:
3x + 1 & \text{for } x \neq -2 \\ 2 & \text{for } x = -2 \end{cases}$$ To find $$f(-2)$$, we use the part of the function where $$x = -2$$. According to the second case: $$f(-2) = 2$$ Thus, $$f(-2) = 2$$. Would you like further details or have any questions? --- Here are 5 related questions to expand on this concept: 1. What is $$f(0)$$ for this function? 2. How would you describe the behavior of this piecewise function as $$x \to -2$$? 3. What would the graph of this piecewise function look like? 4. How can we check the continuity of $$f(x)$$ at $$x = -2$$? 5. What happens if $$f(x)$$ had a different rule for $$x = -2$$? **Tip:** When dealing with piecewise functions, always check which case applies based on the value of $$x$$.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Function Evaluation
Formulas
f(x) = 3x + 1 for x ≠ -2
f(x) = 2 for x = -2
Theorems
Piecewise Function Definition
Suitable Grade Level
Grades 7-9