A function f(x)
 includes the points (2, 3)
, (−5, 1)
, and (10, −3)
 in its graph. Based on this, which of the following points must be included in the graph of f−1(x)
?

Choose TWO correct answers. 
A.(3, 4)

B.(−3, 10)

C.(−1, 5)

D.(−3, −2)

E.(−5, 1)

F.(3, 2)


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.

A function f(x) includes the points (2, 3), (−5, 1), and (10, −3) in its graph. Based on this, which of the following points must be included in the graph of f−1(x)? Choose TWO correct answers. A.(3, 4), B.(−3, 10), C.(−1, 5), D.(−3, −2), E.(−5, 1), F.(3, 2)

This problem helps you learn how to identify points on the inverse of a function. Given points (2, 3), (−5, 1), and (10, −3) on the graph of f(x), find corresponding points on f−1(x). Learn to apply the property of inverse functions by swapping coordinates. Suitable for Grades 10-12.

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