Math Problem Statement
Given the following piecewise function, evaluate f(3). f(x) = {7x + 1 if x < 3; -5x + 5 if x ≥ 3}
Solution
The given problem is asking to evaluate for a piecewise function defined as:
\begin{cases} 7x + 1 & \text{if } x < 3 \\ -5x + 5 & \text{if } x \geq 3 \end{cases}$$ To solve for $$f(3)$$: - Since $$x = 3$$, we need to use the second part of the piecewise function, where $$x \geq 3$$. The expression for this case is $$-5x + 5$$. Substitute $$x = 3$$ into the second equation: $$f(3) = -5(3) + 5 = -15 + 5 = -10$$ Thus, $$f(3) = -10$$, which matches the provided answer. Let me know if you'd like further details or explanations! Here are some related questions for practice: 1. How would you evaluate $$f(2)$$ for the given function? 2. What is the general form of a piecewise function? 3. What are common applications of piecewise functions? 4. How would the function change if the condition for $$f(x)$$ was $$x \leq 3$$ instead of $$x < 3$$? 5. Can a piecewise function be continuous at the boundary point (e.g., $$x = 3$$)? **Tip:** Always pay close attention to the boundary conditions in piecewise functions. They determine which part of the function you should use!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Substitution
Algebra
Formulas
f(x) = {7x + 1 if x < 3; -5x + 5 if x ≥ 3}
Substitute x into the appropriate part of the piecewise function
Theorems
Definition of piecewise functions
Suitable Grade Level
Grade 9-10