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).