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It looks like you've uploaded a photo of a set of calculus problems. Let's focus on solving Problem 15, which asks about inverse functions. Here's the breakdown:

### Problem 15:
Assume that \( f \) is a one-to-one function.

#### (a) If \( f(6) = 17 \), what is \( f^{-1}(17) \)?

- **Solution**: Since \( f^{-1} \) is the inverse of \( f \), it undoes what \( f \) does. So, if \( f(6) = 17 \), then by definition of the inverse function:
  \[
  f^{-1}(17) = 6
  \]

#### (b) If \( f^{-1}(3) = 2 \), what is \( f(2) \)?

- **Solution**: This tells us that \( f^{-1}(3) = 2 \), meaning \( f(2) = 3 \) (since the inverse function undoes the original function):
  \[
  f(2) = 3
  \]

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Let me know if you'd like further details or have any questions. Here are five related questions to help you practice:

1. If \( f(a) = b \), what is \( f^{-1}(b) \)?
2. What property must a function have to have an inverse?
3. If \( f(x) = 2x + 3 \), find \( f^{-1}(x) \).
4. Given \( f(10) = 5 \), what is \( f^{-1}(5) \)?
5. If \( f^{-1}(4) = 7 \), what is \( f(7) \)?

### Tip:
For a function to have an inverse, it must be **one-to-one** (bijective), meaning each output is linked to exactly one input.

Assume that f is a one-to-one function. (a) If f(6) = 17, what is f^{-1}(17)? (b) If f^{-1}(3) = 2, what is f(2)?

Learn how to find the inverse of a one-to-one function, using the given values for f(6) = 17 and f^{-1}(3) = 2. This problem covers key concepts of inverse functions and their properties. Suitable for advanced high school or introductory college-level calculus students.

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