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The question asks for the inverse of the function \( f(x) = 4x - 6 \). Let's find the inverse function \( f^{-1}(x) \).

### Steps to find the inverse:

1. Start with the function:
   \[
   y = 4x - 6
   \]

2. Swap \( x \) and \( y \):
   \[
   x = 4y - 6
   \]

3. Solve for \( y \):
   \[
   x + 6 = 4y
   \]
   \[
   y = \frac{x + 6}{4}
   \]

Thus, the inverse function is:
\[
f^{-1}(x) = \frac{x + 6}{4}
\]

Now, let's compare this with the answer choices:

- a. \( \frac{1}{4}(6 - x) \)
- b. \( \frac{1}{4}(6 + x) \)
- c. \( -\frac{1}{4}(x - 6) \)
- d. \( \frac{1}{4}(x + 6) \)
- e. \( -\frac{1}{4}(6 - x) \)

The correct answer is **d. \( \frac{1}{4}(x + 6) \)**.

Would you like any further clarification or details on this?

### Here are five related questions to practice:
1. What is the inverse of the function \( f(x) = 3x + 5 \)?
2. How do you verify that two functions are inverses of each other?
3. If \( f(x) = 2x - 4 \), what is \( f^{-1}(x) \)?
4. What happens to the graph of a function when you take its inverse?
5. Can all functions have an inverse? Why or why not?

### Tip:
When finding the inverse of a function, always remember to swap \( x \) and \( y \), and then solve for \( y \).

Inverse dari fungsi f(x) = 4x - 6 adalah f^(-1)(x) = ...

Learn how to find the inverse of the function f(x) = 4x - 6 with a step-by-step solution. This problem introduces key algebraic concepts, such as inverse functions and linear equations. Suitable for high school students.

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