Math Problem Statement
Find f(5) for the piecewise function:
f(x) = {
-(x - 4)^2, for x ≠ 5
3, for x = 5
}
Solution
The problem asks us to find from the given piecewise function:
\begin{cases} -(x - 4)^2 & \text{for } x \neq 5, \\ 3 & \text{for } x = 5. \end{cases}$$ ### Solution: To find $$f(5)$$, we refer to the second case in the definition of the function: - When $$x = 5$$, $$f(x) = 3$$. ### Final Answer: $$f(5) = 3$$ --- Would you like me to analyze the continuity of this function or explain its behavior further? Let me know! --- ### Related Questions: 1. What is the value of $$f(x)$$ when $$x = 6$$? 2. Is this function continuous at $$x = 5$$? Why or why not? 3. What is the behavior of $$-(x - 4)^2$$ for $$x > 4$$? 4. Can you plot the graph of $$f(x)$$ for $$x \neq 5$$? 5. How would $$f(x)$$ change if $$f(5)$$ were defined differently, say $$f(5) = -2$$? ### Tip: When solving piecewise functions, always check which condition applies based on the value of $$x$$.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Substitution
Evaluating Functions
Formulas
f(x) = -(x - 4)^2
f(x) = c (constant) for x = 5
Theorems
Definition of Piecewise Functions
Suitable Grade Level
Grades 9-12