Math Problem Statement
f(x) = { x for x ≠ 5, -5 for x = 5 }, Find f(7)
Solution
The function is a piecewise function defined as:
x & \text{for } x \neq 5 \\ -5 & \text{for } x = 5 \end{cases}$$ You are asked to find $$f(7)$$. Since $$7 \neq 5$$, we use the first case of the piecewise function, which tells us that $$f(x) = x$$ for $$x \neq 5$$. Thus, $$f(7) = 7$$ Let me know if you'd like further clarification or a breakdown of the steps! --- Here are five related questions for further exploration: 1. What is $$f(5)$$ for this function? 2. How would the function behave for negative values like $$f(-3)$$? 3. What is the domain and range of the function $$f(x)$$? 4. How would you graph this piecewise function? 5. Can you modify the piecewise function to handle a different value for $$x = 5$$? **Tip:** Always check which condition in a piecewise function applies before plugging in a value for $$x$$.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Function Evaluation
Formulas
f(x) = x for x ≠ 5
f(x) = -5 for x = 5
Theorems
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Suitable Grade Level
Grades 9-12