
Brody wants to write the inverse function of y = 3x − 8. Which of the following is mathematically equivalent to the inverse function?

To find the inverse of the function \( y = 3x - 8 \), we follow these steps:

### Step 1: Replace \( y \) with \( f(x) \)
We start with:
\[
y = 3x - 8
\]
We replace \( y \) with \( f(x) \):
\[
f(x) = 3x - 8
\]

### Step 2: Switch \( x \) and \( y \)
Now, to find the inverse, switch the roles of \( x \) and \( y \):
\[
x = 3y - 8
\]

### Step 3: Solve for \( y \)
Now, solve for \( y \) (this will give us the inverse function):
\[
x + 8 = 3y
\]
\[
y = \frac{x + 8}{3}
\]

Thus, the inverse function is:
\[
f^{-1}(x) = \frac{x + 8}{3}
\]

### Conclusion:
The inverse function of \( y = 3x - 8 \) is \( f^{-1}(x) = \frac{x + 8}{3} \).

Would you like more details or have any other questions?

Here are 5 related questions to expand your understanding:

1. What is the general process for finding the inverse of a function?
2. How do we verify that two functions are inverses of each other?
3. What happens if the function is not one-to-one? Can we still find an inverse?
4. How do we interpret the inverse function graphically?
5. What are real-life applications of inverse functions?

**Tip**: Always check if a function is **one-to-one** (passes the horizontal line test) before trying to find its inverse.

Brody wants to write the inverse function of y = 3x − 8. Which of the following is mathematically equivalent to the inverse function?

Learn how to find the inverse function of y = 3x - 8 with a detailed, step-by-step explanation. This problem involves key algebraic concepts such as functions, inverse functions, and solving for variables. Ideal for students in Grades 9-11.

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