Math Problem Statement

Find f(-3) for the following piecewise-defined function: f(x) = { 4x + 3 if x < 3; -3x + 1 if 3 ≤ x ≤ 9; 2x - 1 if x > 9 }

Solution

The problem asks to find f(3)f(-3) for a piecewise-defined function:

4x + 3 & \text{if } x < 3 \\ -3x + 1 & \text{if } 3 \leq x \leq 9 \\ 2x - 1 & \text{if } x > 9 \end{cases}$$ We are given $$x = -3$$, and since $$-3 < 3$$, we need to use the first piece of the function, $$f(x) = 4x + 3$$. Substitute $$x = -3$$ into the equation: $$f(-3) = 4(-3) + 3 = -12 + 3 = -9$$ Thus, $$f(-3) = -9$$. Would you like more details or have any questions? Here are 5 related questions: 1. What is $$f(2)$$ for the same piecewise-defined function? 2. What would be $$f(4)$$ based on the given function? 3. How would you find the value of $$f(10)$$? 4. How can you determine which piece of the function to use for any given $$x$$? 5. Can a piecewise function have overlapping intervals? **Tip**: Always double-check which interval the input value falls into before substituting into a piecewise function.

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Math Problem Analysis

Mathematical Concepts

Piecewise Functions
Algebra
Linear Equations

Formulas

f(x) = 4x + 3 for x < 3
f(x) = -3x + 1 for 3 ≤ x ≤ 9
f(x) = 2x - 1 for x > 9

Theorems

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Suitable Grade Level

Grades 8-10