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To find the inverse of the given function \( f(x) = 2x - 4 \), follow these steps:

1. Replace \( f(x) \) with \( y \):
   \[
   y = 2x - 4
   \]

2. Swap \( x \) and \( y \) to find the inverse:
   \[
   x = 2y - 4
   \]

3. Solve for \( y \):
   \[
   x + 4 = 2y
   \]
   \[
   y = \frac{x + 4}{2}
   \]

Thus, the inverse function is:
\[
f^{-1}(x) = \frac{x + 4}{2}
\]

Would you like further details or have any questions?

Here are five related questions:
1. How can you verify that two functions are inverses of each other?
2. What are the conditions for a function to have an inverse?
3. How does the graph of a function compare to its inverse?
4. Can all linear functions have an inverse?
5. What happens to the domain and range when finding the inverse?

**Tip:** Always check if a function is one-to-one (bijective) before finding its inverse; a function must be one-to-one to ensure the inverse exists.

Learn how to find the inverse of the function f(x) = 2x - 4. This step-by-step solution explores algebraic concepts and the process for finding the inverse. Suitable for students in Grades 9-12.

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