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To determine which graph represents the inverse of the given function \( f(x) \):

### Observations:
1. The graph of \( f(x) \) is increasing and appears to have a logarithmic shape.
2. The inverse graph, \( f^{-1}(x) \), will be a reflection of \( f(x) \) across the line \( y = x \).

### Process:
- Look for a graph that is symmetric with \( f(x) \) across the line \( y = x \).
- The inverse graph should start near the y-axis and rise more slowly as \( x \) increases, resembling an exponential growth function.

### Matching:
- Upon inspecting the provided options, the second graph (option B) appears to satisfy the reflection symmetry about \( y = x \). This is because:
  - The graph begins steeply and flattens as \( x \) increases, typical of exponential growth (inverse of logarithmic behavior).

### Conclusion:
The correct graph of \( f^{-1}(x) \) is **option B**.

Would you like me to explain any of the steps further? 

Here are five related questions for deeper understanding:
1. What does it mean for two functions to be inverses of each other?
2. How do you algebraically determine the inverse of a given function?
3. What are the common characteristics of exponential and logarithmic functions?
4. Why do inverse functions reflect across the line \( y = x \)?
5. Can a function that is not one-to-one have an inverse?

**Tip:** To verify a graph represents the inverse of another, check that the points \( (a, b) \) on one graph correspond to \( (b, a) \) on the other!

Which of the following is the graph of the inverse of function f?

Learn how to determine the graph of the inverse of a logarithmic function by reflecting it across the line y = x. Includes detailed explanation of the steps and characteristics of inverse functions. Suitable for Grades 9-12.

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