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To solve this problem, let's go through the details step by step:

The problem states:  
"If \( f \) is a one-to-one function such that \( f(2) = -8 \), what is \( f^{-1}(-8) \)?"

Given information:
- \( f(2) = -8 \) means when you input 2 into the function \( f \), the output is -8.
- A one-to-one function has a unique inverse, \( f^{-1} \), such that if \( f(a) = b \), then \( f^{-1}(b) = a \).

Therefore, if \( f(2) = -8 \), then:
\[
f^{-1}(-8) = 2.
\]

Thus, the answer is \( 2 \).

Would you like more details or have any questions?

Here are some related questions to expand your understanding:
1. What are the properties of one-to-one functions?
2. How do you find the inverse of a function?
3. What does it mean for a function to have an inverse?
4. How can you determine if a function is one-to-one?
5. How do you solve problems involving inverse functions graphically?

**Tip:** For a function to have an inverse, it must be both one-to-one (each input maps to a unique output) and onto (every possible output is mapped from some input).

If f is a one-to-one function such that f(2) = -8, what is f^(-1)(-8)?

Learn how to find the inverse of a one-to-one function, given f(2) = -8. This problem covers key concepts such as functions, inverse functions, and the one-to-one property. Suitable for students in Grades 9-12.

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