Math Problem Statement

Find f(-2) for the piece-wise function f(x) = {x+2 if x < 1, x-1 if x ≥ 1}.

Solution

The given piecewise function is defined as:

x + 2 & \text{if } x < 1 \\ x - 1 & \text{if } x \geq 1 \end{cases}$$ We are asked to find $$f(-2)$$. ### Step-by-step solution: 1. First, observe that $$-2$$ is less than 1, so we use the first part of the piecewise function: $$f(x) = x + 2$$. 2. Substitute $$x = -2$$ into the function: $$f(-2) = -2 + 2 = 0$$ So, $$f(-2) = 0$$. The correct answer is $$0$$. Would you like more details or have any questions about this? Here are five related questions to expand the concept: 1. What happens to $$f(x)$$ when $$x = 0$$? 2. What is the value of $$f(x)$$ for $$x = 1$$? 3. How would the graph of this piecewise function look for all $$x$$? 4. Can you determine $$f(x)$$ if $$x = 5$$? 5. What is the domain and range of this piecewise function? **Tip:** Always pay attention to the conditions that determine which part of a piecewise function to use for a given value of $$x$$.

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Math Problem Analysis

Mathematical Concepts

Piecewise Functions
Basic Algebra

Formulas

f(x) = x + 2 for x < 1
f(x) = x - 1 for x ≥ 1

Theorems

Piecewise Function Evaluation

Suitable Grade Level

Grades 6-8