Math Problem Statement

Find f(-1) for the given piecewise function.

Solution

To find f(1)f(-1) from the piecewise function:

\begin{cases} 2x + 8 & \text{for } -5 \leq x < -1 \\ -6 & \text{for } x = -1 \\ x + 5 & \text{for } -1 < x \leq 2 \end{cases}$$ We are specifically asked to find $$f(-1)$$. According to the second part of the piecewise definition, when $$x = -1$$, the function value is: $$f(-1) = -6$$ Therefore, $$f(-1) = -6$$. Would you like a detailed explanation of how to handle similar piecewise functions or explore another aspect of this problem? Here are some related questions: 1. How do you graph a piecewise function like this one? 2. What is the domain and range of the given piecewise function? 3. How do you determine continuity at $$x = -1$$ for this function? 4. Can we evaluate $$f(x)$$ for any other value of $$x$$? 5. How would the function change if the intervals were different? **Tip:** Always check the intervals carefully when evaluating piecewise functions to ensure you're using the correct expression!

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Math Problem Analysis

Mathematical Concepts

Piecewise Functions
Function Evaluation

Formulas

f(x) = 2x + 8 for -5 ≤ x < -1
f(x) = -6 for x = -1
f(x) = x + 5 for -1 < x ≤ 2

Theorems

Piecewise Function Definition

Suitable Grade Level

Grades 9-12