To find the inverse of the function \( f(x) = \frac{1}{x} + 15 \), follow these steps:

1. Replace \( f(x) \) with \( y \):
   \[
   y = \frac{1}{x} + 15
   \]

2. Swap \( x \) and \( y \) (since we want to solve for the inverse):
   \[
   x = \frac{1}{y} + 15
   \]

3. Solve for \( y \):
   - Subtract 15 from both sides:
     \[
     x - 15 = \frac{1}{y}
     \]
   - Take the reciprocal of both sides to isolate \( y \):
     \[
     y = \frac{1}{x - 15}
     \]

Thus, the inverse function is:
\[
f^{-1}(x) = \frac{1}{x - 15}
\]

Would you like further details or explanations?

Here are 5 related questions to expand your understanding:
1. How do you verify that two functions are inverses of each other?
2. What is the domain of the inverse function \( f^{-1}(x) = \frac{1}{x - 15} \)?
3. What happens to the inverse function if the original function has an additional transformation?
4. How would you graph both \( f(x) \) and \( f^{-1}(x) \)?
5. Can an inverse function always exist for any given function?

**Tip:** Always check the domain and range of the function and its inverse, as not all functions are invertible over their entire domain.

Learn how to find the inverse of the function f(x) = 1/x + 15 with a step-by-step guide. This problem covers key algebraic concepts such as inverse functions and solving rational expressions. Ideal for students in Grades 10-12.

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