What is the inverse function of f(x) = 3x - 5

To find the inverse function of \( f(x) = 3x - 5 \), we need to follow these steps:

1. **Replace \( f(x) \) with \( y \):**

   \[
   y = 3x - 5
   \]

2. **Swap \( x \) and \( y \)** (this is because the inverse function reverses the roles of input and output):

   \[
   x = 3y - 5
   \]

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

   \[
   x + 5 = 3y
   \]

   \[
   y = \frac{x + 5}{3}
   \]

4. **Replace \( y \) with \( f^{-1}(x) \) to denote the inverse function:**

   \[
   f^{-1}(x) = \frac{x + 5}{3}
   \]

Thus, the inverse function is:

\[
f^{-1}(x) = \frac{x + 5}{3}
\]

Would you like further details or explanations on any step?

Here are 5 related questions to explore:

1. How do you check if two functions are inverses of each other?
2. What is the domain and range of \( f^{-1}(x) = \frac{x + 5}{3} \)?
3. What happens if a function isn't one-to-one? Can it have an inverse?
4. How would the process change for a more complicated linear function?
5. How do inverse functions relate to graphing?

**Tip:** When finding the inverse, always swap the variables and then solve for the new output.

What is the inverse function of f(x) = 3x - 5?

Learn how to find the inverse function of f(x) = 3x - 5 through a clear, step-by-step process. This guide covers key algebraic concepts, such as function manipulation and inverse functions, suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation