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In part (a), the inverse function of \( f(x) = 2x - 6 \) was correctly found to be:

\[
f^{-1}(x) = \frac{x + 6}{2}
\]

For part (b), the graphs of a function and its inverse are symmetric with respect to the line \( y = x \). This is a general property of inverse functions.

Thus, the answer for part (b) is:

\[
y = x
\]

Would you like further details or have any other questions?

Here are five related questions to deepen your understanding:

1. How do you verify if two functions are inverses of each other?
2. Can you explain why the symmetry between \( f(x) \) and \( f^{-1}(x) \) occurs along the line \( y = x \)?
3. What is the graphical interpretation of an inverse function?
4. How do you determine if a function has an inverse function?
5. What happens if a function is not one-to-one? Can it still have an inverse?

**Tip:** To check if two functions are inverses, compose them (i.e., find \( f(f^{-1}(x)) \) and \( f^{-1}(f(x)) \)) and verify that both simplify to \( x \).

Find the inverse function of f(x) = 2x - 6 and identify the line of symmetry for the graphs of f and its inverse.

Learn how to find the inverse function of f(x) = 2x - 6 and identify the line of symmetry between the function and its inverse. Suitable for students in Grades 10-12, this problem covers essential algebraic concepts, including inverse functions and symmetry.

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