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

A.y=13x−8y=13x−8

B.y=3x−8y=3x−8

C.−y=−3x+8−y=−3x+8

D.x=3y−8x=3y−8


To find the inverse function, we need to swap the roles of \( x \) and \( y \) in the original equation and then solve for \( y \).

The original function is given as:

\[
y = 3x - 8
\]

1. **Swap \( x \) and \( y \):**

\[
x = 3y - 8
\]

2. **Solve for \( y \):**

\[
x + 8 = 3y
\]

\[
y = \frac{x + 8}{3}
\]

So, the inverse function is:

\[
y = \frac{x + 8}{3}
\]

None of the options provided directly matches this inverse function. However, if we rewrite this expression:

\[
y = \frac{1}{3}(x + 8)
\]

Or equivalently:

\[
y = \frac{1}{3}x + \frac{8}{3}
\]

There seems to be a formatting issue in the options provided. Please double-check the answer choices, or I can help you further if they are formatted correctly.

**Do you want more details or have any questions?**  
Here are 5 related questions:

1. How do you derive the inverse of a function in general?
2. What are some applications of inverse functions?
3. How do you verify if two functions are inverses of each other?
4. What does the graph of an inverse function look like compared to the original?
5. What happens to the domain and range when you find an inverse function?

**Tip:** Always double-check your algebraic manipulations when finding inverse functions to avoid mistakes in the final expression.

Brody wants to write the inverse function of y = 3x - 8. Which of the following is mathematically equivalent to the inverse function?
A.y=13x−8
B.y=3x−8
C.−y=−3x+8
D.x=3y−8

Explore how to find the inverse function of y = 3x - 8 with a step-by-step solution. This problem involves algebraic manipulation and understanding inverse functions. Suitable for students in Grades 9-12.

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