To find the inverse of the function \( f(x) = 3x - 6 \), follow these steps:

1. **Replace \( f(x) \) with \( y \):**
   \[
   y = 3x - 6
   \]

2. **Swap \( x \) and \( y \):**
   \[
   x = 3y - 6
   \]

3. **Solve for \( y \):**
   - Add 6 to both sides:
     \[
     x + 6 = 3y
     \]
   - Divide both sides by 3:
     \[
     y = \frac{x + 6}{3}
     \]

4. **Replace \( y \) with \( f^{-1}(x) \):**
   \[
   f^{-1}(x) = \frac{x + 6}{3}
   \]

So, the inverse of \( f(x) = 3x - 6 \) is \( f^{-1}(x) = \frac{x + 6}{3} \).

Would you like more details or have any questions?

Here are 5 related questions:

1. What is the inverse of \( 2x + 3 \)?
2. How do you find the inverse of a quadratic function?
3. What are the conditions for a function to have an inverse?
4. Can you explain the graphical interpretation of a function and its inverse?
5. How does the composition of a function and its inverse relate to identity?

**Tip:** When finding the inverse of a function, ensure that the function is one-to-one (bijective), meaning it passes both the vertical and horizontal line tests.

Learn how to find the inverse of the function f(x) = 3x - 6 with a detailed step-by-step guide. This problem involves functions, inverse functions, and linear equations. Suitable for 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