Math Problem Statement

Q2: f(x) = { 3x - 1, when x ≤ 2; 2, when x > 2 }

Solution

The problem defines a piecewise function:

\begin{cases} 3x - 1 & \text{when } x \leq 2 \\ 2 & \text{when } x > 2 \end{cases}$$ Would you like me to analyze this further (e.g., finding continuity, differentiability, or plotting the function)? Let me know! Here are 5 related questions to explore this function: 1. What is the value of $$f(2)$$ and $$f(3)$$? 2. Is $$f(x)$$ continuous at $$x = 2$$? 3. What is the slope of $$f(x)$$ for $$x \leq 2$$? 4. Can we differentiate $$f(x)$$ at $$x = 2$$? 5. What happens to $$f(x)$$ as $$x \to -\infty$$? **Tip:** For piecewise functions, always check continuity and differentiability at the points where the function changes definition.

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Math Problem Analysis

Mathematical Concepts

Piecewise Functions
Continuity
Differentiability

Formulas

f(x) = 3x - 1 for x ≤ 2
f(x) = 2 for x > 2

Theorems

Definition of Continuity
Definition of Differentiability

Suitable Grade Level

Grades 10-12