https://file.aiquickdraw.com/mathbot/file/1731488766784or7t405t.jpg

To find the domain of the inverse of a function, we should first consider the **range** of the original function, as the range of the function becomes the domain of its inverse.

Looking at the provided graph:

1. The function approaches positive infinity as \( x \to 0^+ \) (from the right side of the y-axis).
2. As \( x \to -\infty \), the function value flattens out, approaching \( y = 0 \).
3. The graph indicates that the function values cover all \( y \)-values from \( -\infty \) to \( 0 \) (exclusive) and from \( 0 \) to \( +\infty \) (exclusive).

Therefore, the range of the function is:
\[
(-\infty, 0) \cup (0, +\infty)
\]

Since this is the range of the function, it will be the **domain of the inverse** of the function.

### Answer:
The domain of the inverse of the function is:
\[
(-\infty, 0) \cup (0, +\infty)
\]

Would you like further details or explanations on any part of this solution?

Here are some related questions for further exploration:

1. What would be the range of the inverse of this function?
2. How do we determine the range of a function if only the graph is given?
3. What are the conditions for a function to have an inverse?
4. How does the vertical asymptote of a function affect the domain of its inverse?
5. Can the inverse of this function be represented as a function itself?

**Tip:** For any function, remember that the domain of its inverse is equivalent to the range of the original function.

The graph of a function is shown in the diagram. Find the domain of the inverse of the function.

Understand how to determine the domain of the inverse of a function by analyzing its graph. This example demonstrates finding the range of the function, which becomes the domain of the inverse, by examining the function's behavior as it approaches specific asymptotes and covers various y-values. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation