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

Choose **TWO** correct answers.

A.(3, 4)(3, 4)

B.(−3, 10)(−3, 10)

C.(−1, 5)(−1, 5)

D.(−3, −2)(−3, −2)

E.(−5, 1)(−5, 1)

F.(3, 2)(3, 2)

To solve this problem, we need to understand that if a function \( f(x) \) contains a point \( (a, b) \), then its inverse function \( f^{-1}(x) \) must include the point \( (b, a) \). This means the x and y values are swapped in the inverse function.

The points provided for \( f(x) \) are:
- \( (2, 3) \)
- \( (-5, 1) \)
- \( (10, -3) \)

For the inverse function \( f^{-1}(x) \), the corresponding points will be:
- \( (3, 2) \) from \( (2, 3) \)
- \( (1, -5) \) from \( (-5, 1) \)
- \( (-3, 10) \) from \( (10, -3) \)

Now, let's check which points match these in the options provided:
- B. \( (-3, 10) \)
- F. \( (3, 2) \)

So, the correct answers are:

**B and F**.

Would you like further clarification or details?

Here are 5 questions to deepen understanding:
1. What is the relationship between a function and its inverse?
2. How do we identify points in the inverse function graph?
3. How would the point \( (7, 4) \) in \( f(x) \) transform in \( f^{-1}(x) \)?
4. Can a function have more than one inverse?
5. What conditions must a function satisfy to have an inverse?

**Tip:** Always remember that the graph of a function and its inverse are reflections across the line \( y = x \).

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)

Solve a problem involving inverse functions by identifying corresponding points. If f(x) includes (2, 3), (−5, 1), and (10, −3), the inverse f−1(x) will contain (3, 2), (1, −5), and (−3, 10). Learn how to swap coordinates and understand the relationship between a function and its inverse. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation