Math Problem Statement
Find f(7) for the function f(x) = { x for x ≠ 5, -5 for x = 5 }.
Solution
The given function is defined as a piecewise function:
x & \text{for } x \neq 5 \\ -5 & \text{for } x = 5 \end{cases}$$ We are tasked with finding $$f(7)$$. Since $$7 \neq 5$$, we use the first part of the piecewise function, where $$f(x) = x$$. Therefore: $$f(7) = 7$$ The answer is $$f(7) = 7$$. Would you like any further explanation or details? Here are some related questions to extend this concept: 1. What is $$f(5)$$ based on the same function? 2. How would you graph this piecewise function? 3. What is the general behavior of piecewise functions around a discontinuity, like at $$x = 5$$ here? 4. How would you describe the domain and range of this function? 5. How do you find limits for piecewise functions at points of discontinuity? **Tip:** When working with piecewise functions, always check which part of the function applies to the value of $$x$$ before plugging in.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Basic Algebra
Formulas
f(x) = { x for x ≠ 5, -5 for x = 5 }
Theorems
Basic Definition of Piecewise Functions
Suitable Grade Level
Grades 9-12