Math Problem Statement

Given the piecewise function h(x) = { -3x, x < 2; 4x + 1, x >= 2 }, find the value of 3h(-2).

Solution

The piecewise function given in the image is:

\begin{cases} -3x, & \text{if } x < 2 \\ 4x + 1, & \text{if } x \geq 2 \end{cases}$$ We need to find the value of $$3h(-2)$$. ### Step 1: Find $$h(-2)$$ Since $$-2 < 2$$, we use the first part of the piecewise function, $$h(x) = -3x$$. $$h(-2) = -3(-2) = 6$$ ### Step 2: Multiply by 3 to get $$3h(-2)$$ $$3h(-2) = 3 \times 6 = 18$$ Thus, the value of $$3h(-2)$$ is $$\boxed{18}$$, which matches the selected answer. Would you like any further explanation or details? Here are five related questions for further practice: 1. What is the value of $$h(2)$$? 2. Find the value of $$2h(1)$$. 3. What is the domain of the function $$h(x)$$? 4. Evaluate $$h(0)$$ and $$h(3)$$. 5. For what values of $$x$$ does $$h(x) = 1$$? **Tip:** Always carefully check which part of a piecewise function applies to the given input value!

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Math Problem Analysis

Mathematical Concepts

Piecewise Functions
Basic Algebra

Formulas

h(x) = -3x for x < 2
h(x) = 4x + 1 for x >= 2

Theorems

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Suitable Grade Level

Grades 9-10