Math Problem Statement
u(x)= 2x+8 if x>2 5x-2 if x greater than or equal u(-2)
Solution
We are given a piecewise function defined as:
\begin{cases} 2x + 8 & \text{if } x > 2 \\ 5x - 2 & \text{if } x \leq 2 \end{cases}$$ We are asked to evaluate $$u(-2)$$. Since $$-2 \leq 2$$, we use the second part of the function: $$u(x) = 5x - 2$$ Substitute $$x = -2$$: $$u(-2) = 5(-2) - 2 = -10 - 2 = -12$$ Thus, $$u(-2) = -12$$. Would you like more details or have any further questions? Here are 5 related questions to explore further: 1. How would the function change if $$u(x)$$ were defined differently for $$x \leq 2$$? 2. What is $$u(2)$$ based on this piecewise function? 3. Can you graph this piecewise function, and what does the graph look like? 4. How does the function behave as $$x$$ approaches 2 from the left and right? 5. What is the domain and range of $$u(x)$$? **Tip:** Always check which condition applies to the given $$x$$ value before substituting into a piecewise function.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Linear Equations
Substitution
Formulas
u(x) = 2x + 8 for x > 2
u(x) = 5x - 2 for x ≤ 2
Theorems
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Suitable Grade Level
Grades 8-10