Math Problem Statement

f(x) = {5 for x ≠ 1, 1 for x = 1}. Find f(2).

Solution

The problem provided shows a piecewise function defined as:

\begin{cases} 5 & \text{for } x \neq 1 \\ 1 & \text{for } x = 1 \end{cases}$$ You are tasked with finding $$f(2)$$. ### Solution: 1. From the definition of the function, when $$x \neq 1$$, $$f(x) = 5$$. 2. Since $$2 \neq 1$$, the condition $$x \neq 1$$ applies. 3. Therefore, $$f(2) = 5$$. ### Final Answer: $$f(2) = 5$$ Let me know if you'd like additional details or have any questions! Below are five related questions for deeper exploration: --- ### Related Questions: 1. What is the value of $$f(1)$$ for this function, and why? 2. How would the graph of this piecewise function look? 3. Can you generalize what $$f(x)$$ equals for any $$x > 1$$? 4. How does the function behave if $$x \to 1$$ from the left or the right? 5. Is the function $$f(x)$$ continuous at $$x = 1$$? Why or why not? --- ### Tip: Always pay attention to the conditions of a piecewise function, as they define how the function behaves for different values of $$x$$.

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Math Problem Analysis

Mathematical Concepts

Piecewise Functions
Function Evaluation

Formulas

Piecewise Function Definition

Theorems

Substitution Rule for Function Evaluation

Suitable Grade Level

Grades 9-12