Math Problem Statement
Evaluate f(-2) if f(x) = { 2 - 3(x - 1) if x ≤ -1, 5 + x^2 if x > -1 }
Solution
The question asks to evaluate for the given piecewise function:
2 - 3(x - 1) & \text{if } x \leq -1 \\ 5 + x^2 & \text{if } x > -1 \end{cases}$$ Since $$-2 \leq -1$$, we use the first case of the function: $$f(x) = 2 - 3(x - 1)$$ Now substitute $$x = -2$$: $$f(-2) = 2 - 3(-2 - 1)$$ $$f(-2) = 2 - 3(-3)$$ $$f(-2) = 2 + 9 = 11$$ Thus, $$f(-2) = 11$$. Let me know if you'd like more details or if you have any questions! ### Related Questions: 1. How do you handle piecewise functions when evaluating limits? 2. Can you explain how to graph a piecewise function like this one? 3. What is the domain and range of this piecewise function? 4. How do you differentiate a piecewise function? 5. Can the function given be continuous? If so, at which points? **Tip:** Always check which condition of a piecewise function applies before substituting values.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Substitution
Formulas
f(x) = 2 - 3(x - 1) for x ≤ -1
f(x) = 5 + x^2 for x > -1
Theorems
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Suitable Grade Level
Grades 9-11