For a function $f(x)$ and its inverse $f^{-1}(x)$, the points on the graph of $f$ and $f^{-1}$ are related in a very specific way. If $f(a) = b$, then $f^{-1}(b) = a$. Essentially, the $x$- and $y$-coordinates of each point on the graph of $f$ are swapped for the corresponding point on the graph of $f^{-1}$.

Given that $f(x)$ includes the points $(2, 3)$, $(-5, 1)$, and $(10, -3)$, their corresponding points on $f^{-1}(x)$ will be:

• $(2, 3)$ on $f(x)$ becomes $(3, 2)$ on $f^{-1}(x)$.
• $(-5, 1)$ on $f(x)$ becomes $(1, -5)$ on $f^{-1}(x)$.
• $(10, -3)$ on $f(x)$ becomes $(-3, 10)$ on $f^{-1}(x)$.

Thus, the correct points that must be included in the graph of $f^{-1}(x)$ are:

• B. (-3, 10)
• F. (3, 2)

Would you like further clarification or details?

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Here are 5 related questions to further explore this concept:

1. How do you find the inverse of a function algebraically?
2. Can every function have an inverse? Why or why not?
3. What conditions must a function meet for its inverse to also be a function?
4. What are the graphical properties of a function and its inverse?
5. How do domain and range relate between a function and its inverse?

Tip: A function must be bijective (both injective and surjective) to have an inverse that is also a function.