To solve for the inverse of the function \( f(x) = \frac{x}{3} \), we need to follow these steps:

### Steps to Find the Inverse Function

1. **Start with the function** \( f(x) = \frac{x}{3} \).
   
2. **Rewrite the function in terms of \( y \)**:  
   \[
   y = \frac{x}{3}
   \]
   
3. **Swap** \( x \) and \( y \). This is because, for the inverse function, we want to solve for \( y \) in terms of \( x \). So:
   \[
   x = \frac{y}{3}
   \]

4. **Solve for \( y \)**:
   Multiply both sides of the equation by 3 to isolate \( y \):
   \[
   y = 3x
   \]

5. **Write the inverse function**:  
   The inverse function is:
   \[
   f^{-1}(x) = 3x
   \]

### Final Answer:
The inverse function of \( f(x) = \frac{x}{3} \) is:
\[
f^{-1}(x) = 3x
\]

Would you like a more detailed explanation, or do you have any specific questions?

---

Here are 5 related questions to expand your understanding:

1. How do you find the inverse of a more complex linear function?
2. What is the geometric interpretation of a function and its inverse?
3. How can you verify that two functions are inverses of each other?
4. How do the domain and range of a function relate to its inverse?
5. Can every function have an inverse? Why or why not?

**Tip:** To verify if two functions are inverses, check if \( f(f^{-1}(x)) = x \) and \( f^{-1}(f(x)) = x \).

Discover how to find the inverse function of f(x) = x/3 with a clear step-by-step solution. This guide explains the algebraic process of finding an inverse function, including key concepts such as swapping variables and solving for y. Perfect for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation