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The problem provides the function \( f(x) = 7x + 6 \), and asks for the value of the inverse function \( f^{-1}(x) \) at \( f^{-1}(27) \).

### Step-by-step solution:

1. Start with the given function \( f(x) = 7x + 6 \).
2. To find the inverse \( f^{-1}(x) \), swap \( f(x) \) with \( y \):
   \[
   y = 7x + 6
   \]
3. Solve for \( x \):
   \[
   y - 6 = 7x
   \]
   \[
   x = \frac{y - 6}{7}
   \]
4. So, the inverse function is:
   \[
   f^{-1}(x) = \frac{x - 6}{7}
   \]
5. Now, calculate \( f^{-1}(27) \):
   \[
   f^{-1}(27) = \frac{27 - 6}{7} = \frac{21}{7} = 3
   \]

Thus, the value of \( f^{-1}(27) \) is \( \boxed{3} \).

Would you like more details or have any questions?

### Related Questions:
1. How do you verify if a function is invertible?
2. What are the conditions for a function to have an inverse?
3. How do you calculate the inverse for a quadratic function?
4. What is the relationship between a function and its inverse graphically?
5. How do you compose a function with its inverse?

**Tip:** The inverse of a linear function always exists as long as the slope is non-zero.

Diketahui f(x) = 7x + 6. Jika invers fungsi f(x) adalah f^{-1}(x), nilai f^{-1}(27) adalah …

Learn how to find the inverse of the linear function f(x) = 7x + 6 and calculate f^{-1}(27). This problem involves key algebraic concepts, including finding inverse functions, and is suitable for students in Grades 10-12.

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