To determine the correct graph of the inverse function $f^{-1}$, we need to follow these steps:

Analysis:

1. The graph of an inverse function is a reflection of the original graph across the line $y = x$. This means:
   • If a point $(a, b)$ is on the original function $f$, then $(b, a)$ will be on $f^{-1}$.
2. Observing the original graph:
   • The curve is a decreasing function (moving downward as $x$ increases) and is entirely below the line $y = x$.
   • The inverse must be a curve that is entirely above the line $y = x$ and symmetric to the original.

Visual Inspection of Choices:

• In option A, the reflected curve across $y = x$ appears correct. This matches the description of the inverse function.
• In options B, C, and D, the symmetry does not align with the $y = x$ reflection.

Conclusion:

The correct answer is A.

Would you like further clarification or detailed reasoning?

Here are some related questions for further exploration:

1. What is the general method for graphing the inverse of any given function?
2. How can you verify algebraically that a function is one-to-one before finding its inverse?
3. What are some real-world examples where the concept of an inverse function is used?
4. How does domain and range change between a function and its inverse?
5. How can you use the derivative to check if a function is invertible?

Tip:

Always check for symmetry across $y = x$ when verifying or sketching the graph of an inverse function.