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The problem asks to find \( f(7) \) for the given piecewise-defined function:

\[
f(x) = 
\begin{cases} 
x + 13 & \text{if } x < 7 \\
-2x + 6 & \text{if } x \geq 7
\end{cases}
\]

Since \( x = 7 \), we use the second condition because \( x \geq 7 \).

Thus, we substitute \( x = 7 \) into the equation \( -2x + 6 \):

\[
f(7) = -2(7) + 6 = -14 + 6 = -8
\]

So, the answer is \( f(7) = -8 \).

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. What is \( f(6) \) for this same piecewise function?
2. How do piecewise functions differ from regular functions?
3. Can piecewise functions be continuous? Under what conditions?
4. How would the graph of this function look near \( x = 7 \)?
5. How do you determine which part of a piecewise function to use?

**Tip:** Always check which condition applies for a given value of \( x \) in piecewise functions.

Find f(7) for this piecewise-defined function: f(x) = {x + 13, if x < 7; -2x + 6, if x ≥ 7}.

Learn how to evaluate a piecewise function at a specific value. This problem demonstrates how to apply conditions in a piecewise function and find f(7) for f(x) = {x + 13 if x < 7; -2x + 6 if x ≥ 7}. Ideal for students in Grades 9-12.

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