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.