Math Problem Statement

Find the inverse of the function y = (5 - 2x) / 3

Solution

The function given in the image is:

y=52x3y = \frac{5 - 2x}{3}

We are tasked to find the inverse of this function.

Steps to Find the Inverse:

  1. Replace yy with xx: x=52y3x = \frac{5 - 2y}{3}

  2. Solve for yy in terms of xx: 3x=52y3x = 5 - 2y 2y=53x2y = 5 - 3x y=53x2y = \frac{5 - 3x}{2}

Inverse Function:

The inverse function is: f1(x)=53x2f^{-1}(x) = \frac{5 - 3x}{2}

Let me know if you'd like further details or a breakdown of the steps!

Here are some related questions to explore:

  1. How do you verify if two functions are inverses of each other?
  2. What is the domain and range of the given function and its inverse?
  3. Can you find the derivative of the inverse function?
  4. How does graphing help in understanding inverses visually?
  5. What are the real-world applications of inverse functions?

Tip: When finding the inverse,

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Inverse Functions

Formulas

y = (5 - 2x) / 3
Inverse function formula

Theorems

Inverse function theorem

Suitable Grade Level

Grades 9-11