Math Problem Statement
Find f(-4) for the given piecewise function f(x) = { (x+6)^2 - 1 for x ≠ -4, 1 for x = -4 }
Solution
The image shows a piecewise function:
(x + 6)^2 - 1 & \text{if } x \neq -4 \\ 1 & \text{if } x = -4 \end{cases}$$ The task is to find $$f(-4)$$. According to the piecewise definition, when $$x = -4$$, the function explicitly defines $$f(-4) = 1$$. Thus, the value of $$f(-4)$$ is $$\boxed{1}$$. Would you like further details or have any additional questions? Here are 5 related questions: 1. What does the term "piecewise function" mean? 2. How would you calculate the value of $$f(x)$$ for $$x = 2$$? 3. What happens if we substitute $$x = -4$$ in the first part of the piecewise function? 4. How can you graph this piecewise function? 5. What is the domain and range of this function? Tip: When working with piecewise functions, always check the condition for each piece to see which one applies to the specific value you're evaluating.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Function Evaluation
Formulas
f(x) = (x+6)^2 - 1 for x ≠ -4
f(x) = 1 for x = -4
Theorems
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Suitable Grade Level
Grades 9-12