https://file.aiquickdraw.com/mathbot/file/1727365494220cvi3ju08.jpg

The table in the image gives the function values \( f(x) \) for specific \( x \)-values, and you are asked to find the corresponding values of the inverse function \( f^{-1}(x) \).

Here is the given data for \( f(x) \):
\[
\begin{array}{c|c}
x & f(x) \\
\hline
-3 & 5 \\
-2 & 4 \\
-1 & 1 \\
0 & -4 \\
1 & 11 \\
\end{array}
\]

To find \( f^{-1}(x) \), recall that for a function and its inverse, \( f^{-1}(f(x)) = x \). This means that if \( f(a) = b \), then \( f^{-1}(b) = a \).

Thus, for the inverse function table:
\[
\begin{array}{c|c}
f(x) & f^{-1}(x) \\
\hline
5 & -3 \\
4 & -2 \\
1 & -1 \\
-4 & 0 \\
11 & 1 \\
\end{array}
\]

The values for \( f^{-1}(x) \) can be filled in as:
- \( f^{-1}(5) = -3 \)
- \( f^{-1}(4) = -2 \)
- \( f^{-1}(1) = -1 \)
- \( f^{-1}(-4) = 0 \)
- \( f^{-1}(11) = 1 \)

Let me know if you need further clarifications!

Here are 5 related questions:
1. How do we determine if a function has an inverse?
2. What conditions must be satisfied for a function to be one-to-one?
3. Can all functions have an inverse function? Why or why not?
4. How is the graph of \( f^{-1}(x) \) related to the graph of \( f(x) \)?
5. How do you algebraically find the inverse of a function?

**Tip:** The graph of a function and its inverse are reflections of each other across the line \( y = x \).

A table of values for f(x) is given. Complete the table for f^{-1}(x) for each corresponding set of values from f(x).

Learn how to find the inverse of a function from a table of values. This problem involves understanding the relationship between a function f(x) and its inverse f^{-1}(x) by applying the formula f^{-1}(f(x)) = x. Suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation