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To determine \( f^{-1}(1) \), we need to understand that the inverse function \( f^{-1}(y) \) gives the value of \( x \) for which \( f(x) = y \).

From the table, when \( f(x) = 1 \), we see that \( x = -4 \).

Thus, \( f^{-1}(1) = -4 \).

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Here are 5 related questions:
1. What is \( f^{-1}(5) \) based on the table?
2. How do we define the inverse of a function?
3. What conditions must a function meet to have an inverse?
4. How do you interpret inverse functions in real-life applications?
5. Can all functions have an inverse?

**Tip:** For a function to have an inverse, it must be **bijective**—that is, both injective (one-to-one) and surjective (onto).

Given the following table of values for the function f(x), determine f^{-1}(1).

Learn how to determine the inverse function value f^{-1}(1) from a table of values. Understand inverse functions and how to solve for x when given f(x). Suitable for students in Grades 9-11.

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