State the inverse function g(x) of this equation: g(x)=3x-2

To find the inverse of the function \( g(x) = 3x - 2 \), we follow these steps:

1. **Rewrite the function using \( y \) instead of \( g(x) \):**
   \[
   y = 3x - 2
   \]

2. **Swap \( x \) and \( y \) to begin the process of finding the inverse:**
   \[
   x = 3y - 2
   \]

3. **Solve for \( y \) (which will be \( g^{-1}(x) \)):**
   \[
   x + 2 = 3y
   \]
   \[
   y = \frac{x + 2}{3}
   \]

Thus, the inverse function is:
\[
g^{-1}(x) = \frac{x + 2}{3}
\]

Would you like any further details or explanations?

Here are five related questions to further explore the concept of inverse functions:
1. How can you verify if two functions are inverses of each other?
2. What happens when you compose a function with its inverse?
3. How would the graph of \( g^{-1}(x) \) compare to the graph of \( g(x) \)?
4. Can every function have an inverse? Why or why not?
5. How does the domain and range of a function affect its inverse?

**Tip:** To check if two functions are inverses, you can compose them and see if the result is the identity function: \( f(g(x)) = x \) and \( g(f(x)) = x \).

Discover how to find the inverse function of g(x) = 3x - 2 using algebraic techniques. This problem covers key concepts in functions and their inverses, with step-by-step solutions. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation