For the function f, of, x, equals, 8, x, minus, 9f(x)=8x−9, find f, to the power minus 1 , left parenthesis, x, right parenthesisf 
−1
 (x).

To find the inverse of the function \( f(x) = 8x - 9 \), denoted as \( f^{-1}(x) \), follow these steps:

### Step 1: Replace \( f(x) \) with \( y \).
\[
y = 8x - 9
\]

### Step 2: Solve for \( x \) in terms of \( y \).
\[
y = 8x - 9
\]
Add 9 to both sides:
\[
y + 9 = 8x
\]
Now, divide both sides by 8:
\[
x = \frac{y + 9}{8}
\]

### Step 3: Replace \( y \) with \( x \) to express the inverse function.
\[
f^{-1}(x) = \frac{x + 9}{8}
\]

Thus, the inverse function is:
\[
f^{-1}(x) = \frac{x + 9}{8}
\]

Would you like further details or have any questions?

Here are 5 related questions you might find useful:
1. How can we verify that \( f(f^{-1}(x)) = x \)?
2. What is the domain and range of \( f(x) = 8x - 9 \)?
3. How do you find the inverse of a quadratic function?
4. What does the inverse function tell us about the original function?
5. How do transformations affect the graph of \( f(x) \) and its inverse?

**Tip:** When finding the inverse, always switch \( x \) and \( y \) and then solve for \( y \).

For the function f(x) = 8x - 9, find the inverse function f^(-1)(x).

Learn how to find the inverse of the linear function f(x) = 8x - 9. This step-by-step guide explores key algebraic concepts, including inverse functions and the inverse function theorem. Suitable for students in Grades 9-11.

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