Math Problem Statement
f(x)=⎩⎨⎧−2x+2−2x+5−(x−6)2−7 for x≤211 for 2<x<611 for x≥611
Find , f, of, 4
Find f(4)
Solution
The function is given piecewise as:
\begin{cases} -2x + 2 & \text{for } x \leq 2 \\ -2x + 5 & \text{for } 2 < x < 6 \\ -(x - 6)^2 - 7 & \text{for } x \geq 6 \end{cases}$$ To find $$f(4)$$, we need to determine which piece of the function applies when $$x = 4$$. Since $$4$$ is between 2 and 6 (i.e., $$2 < 4 < 6$$), we use the second case: $$f(x) = -2x + 5$$ Substitute $$x = 4$$: $$f(4) = -2(4) + 5 = -8 + 5 = -3$$ Thus, $$f(4) = -3$$. Would you like any further details or clarifications? --- Here are five related questions to further explore the topic: 1. What is $$f(2)$$ using the same function? 2. What is the value of $$f(6)$$? 3. How do you find the domain and range of a piecewise function? 4. How do we graph the given piecewise function? 5. Can piecewise functions be continuous? If so, how can we check for continuity? **Tip:** Always check the interval that corresponds to the input value when evaluating piecewise functions!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Function Evaluation
Algebra
Formulas
f(x) = -2x + 2 for x ≤ 2
f(x) = -2x + 5 for 2 < x < 6
f(x) = -(x - 6)^2 - 7 for x ≥ 6
Theorems
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Suitable Grade Level
Grades 9-12