Math Problem Statement
What is the value of f(x) when x = 4 in the piecewise function f(x) = { 4x when x ≤ 4, 2x^2 when x > 4 }?
Solution
The given problem involves a piecewise function , and you need to determine the value of when . The piecewise function is defined as follows:
\begin{cases} 4x & \text{when } x \leq 4 \\ 2x^2 & \text{when } x > 4 \end{cases}$$ To solve for $$f(4)$$, let's substitute $$x = 4$$ into the appropriate piece of the function. Since $$4 \leq 4$$, we use the first piece of the function: $$f(x) = 4x \quad \text{when } x \leq 4$$ Substituting $$x = 4$$: $$f(4) = 4(4) = 16$$ Thus, the value of $$f(4)$$ is $$16$$. The correct answer is $$16$$. Would you like any further details or explanations on this problem? Here are 5 related questions to further explore the topic: 1. What is the value of $$f(x)$$ when $$x = 5$$ in this piecewise function? 2. How does the behavior of the function change for $$x > 4$$? 3. What is the derivative of this piecewise function for $$x \leq 4$$ and $$x > 4$$? 4. How would you graph this piecewise function? 5. Can you find the points of discontinuity for this function, if any? **Tip:** When solving piecewise functions, always check which condition applies to your specific input before substituting values.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Algebra
Formulas
f(x) = 4x when x ≤ 4
f(x) = 2x^2 when x > 4
Theorems
Piecewise Function Evaluation
Suitable Grade Level
Grades 8-10