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The given problem is asking to evaluate \( f(3) \) for a piecewise function defined as:

\[
f(x) =
\begin{cases} 
7x + 1 & \text{if } x < 3 \\
-5x + 5 & \text{if } x \geq 3
\end{cases}
\]

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!

Given the following piecewise function, evaluate f(3). f(x) = {7x + 1 if x < 3; -5x + 5 if x ≥ 3}

Learn how to evaluate the piecewise function f(x) for x = 3 with detailed steps. This problem demonstrates key algebraic skills such as substitution and understanding piecewise-defined functions. Suitable for students in Grades 9-10.

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