Math Problem Statement

What is the range of the inverse function?

Solution

The image you uploaded contains a graph of a function, and the question asks about the range of its inverse function.

To determine the range of the inverse function, remember that the range of the original function becomes the domain of the inverse, and the domain of the original function becomes the range of the inverse.

Looking at the graph:

  • The blue function appears to start at y=4y = 4 and ends at y=2y = 2.
  • The inverse function will have its domain from 2x42 \leq x \leq 4, corresponding to the range of the original function.

Thus, the range of the inverse function corresponds to the domain of the original function. Therefore, the answer is C) 2y42 \leq y \leq 4.

Let me know if you want any further clarifications or details!

Here are some related questions you might find helpful:

  1. What is the definition of the inverse of a function?
  2. How can you graph the inverse of a function?
  3. What is the relationship between the domain and range of a function and its inverse?
  4. How do you find the inverse of a function algebraically?
  5. Can you graph a function and its inverse on the same coordinate plane?

Tip: When solving inverse function problems, always think of switching the roles of xx and yy.

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Math Problem Analysis

Mathematical Concepts

Inverse Functions
Domain and Range

Formulas

Range of the inverse function is the domain of the original function

Theorems

Inverse Function Theorem

Suitable Grade Level

Grades 9-11