To find \( f(x) \), where \( f(2a - 1) = 7a - 13 \), we need to express \( f \) in terms of \( x \) instead of \( a \).

1. Set \( x = 2a - 1 \), so we can write \( f(x) \) instead of \( f(2a - 1) \).
   
   Solving for \( a \) in terms of \( x \):
   \[
   x = 2a - 1
   \]
   \[
   x + 1 = 2a
   \]
   \[
   a = \frac{x + 1}{2}
   \]

2. Substitute \( a = \frac{x + 1}{2} \) into the right side of the given function:
   \[
   f(x) = 7\left(\frac{x + 1}{2}\right) - 13
   \]

3. Simplify this expression:
   \[
   f(x) = \frac{7(x + 1)}{2} - 13
   \]
   \[
   f(x) = \frac{7x + 7}{2} - 13
   \]
   \[
   f(x) = \frac{7x + 7 - 26}{2}
   \]
   \[
   f(x) = \frac{7x - 19}{2}
   \]

Thus, the function is:
\[
f(x) = \frac{7x - 19}{2}
\]

Would you like further clarification on any steps?

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Here are some related questions to deepen understanding:

1. How would the solution change if the function were \( f(3a + 2) = 5a - 8 \)?
2. What is the domain of \( f(x) = \frac{7x - 19}{2} \)?
3. How do we find \( f^{-1}(x) \) for \( f(x) = \frac{7x - 19}{2} \)?
4. How can we check if our answer is correct by substituting values for \( x \)?
5. What does it mean to “solve for \( f(x) \)” in different contexts?

**Tip:** Solving for one variable in terms of another is key to rewriting functions in simpler forms.

Learn how to find f(x) when f(2a − 1) = 7a − 13. This problem demonstrates function substitution and simplification, showing the step-by-step process to express f in terms of x. Ideal for students in Grades 9-10.

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