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The given function \( f(x) \) is defined as a piecewise function:

\[
f(x) = \begin{cases} 
x & \text{for } x \neq 5 \\
-5 & \text{for } x = 5
\end{cases}
\]

We are tasked with finding \( f(7) \).

Since \( 7 \neq 5 \), we use the first part of the piecewise function, where \( f(x) = x \). Therefore:

\[
f(7) = 7
\]

The answer is \( f(7) = 7 \).

Would you like any further explanation or details? Here are some related questions to extend this concept:

1. What is \( f(5) \) based on the same function?
2. How would you graph this piecewise function?
3. What is the general behavior of piecewise functions around a discontinuity, like at \( x = 5 \) here?
4. How would you describe the domain and range of this function?
5. How do you find limits for piecewise functions at points of discontinuity?

**Tip:** When working with piecewise functions, always check which part of the function applies to the value of \( x \) before plugging in.

Find f(7) for the function f(x) = { x for x ≠ 5, -5 for x = 5 }.

Learn how to solve for f(7) using a piecewise function defined as f(x) = { x for x ≠ 5, -5 for x = 5 }. This step-by-step guide covers key algebra concepts such as piecewise functions, suitable for students in Grades 9-12.

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