Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Just questions 5,6,7,8
![**Finding Inverse Functions**
For each function given below, find its inverse and then graph both the function and its inverse.
1. \( f(x) = \sqrt{x - 2} - 2 \)
2. \( g(x) = -2x - 3 \)
3. \( f(x) = \frac{1}{2}x + 1 \)
4. \( h(x) = 2(x - 2)^3 \)
5. \( h(x) = (x + 1)^3 - 3 \)
6. \( g(x) = x + 4 \)
7. \( f(x) = \sqrt[3]{x - 1} + 1 \)
8. \( f(x) = -x - 2 \)
9. \( f(x) = (x - 2)^3 \)
10. \( f(x) = -\frac{3}{5}x + 3 \)
**Find the inverse of each function for \( x > 0 \). Then graph the function and its inverse.**
11. \( y = (x - 1)^2 - 4 \)
12. \( y = 2(x - 1)^2 + 1 \)
13. \( y = -2(x - 4)^2 - 2 \)
14. \( y = -(x - 2)^2 - 1 \)
### Explanation of Graphs and Diagrams
No graphs or diagrams are provided in the image. For each function, you will need to:
1. Solve for the inverse function \( f^{-1}(x) \) or \( y^{-1} = f^{-1}(x) \).
2. Plot the original function and its inverse function on the same coordinate plane.
3. Verify that the graphs are symmetrical with respect to the line \( y = x \), which is a characteristic feature of inverse functions.
These exercises will help in visualizing the concept of inverse functions and their graphical representation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61a624e8-9805-4882-bd7c-8b439f9ba0a9%2F7b82054c-4627-4a8f-8cac-9e17529b1fe0%2Fqt66qg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding Inverse Functions**
For each function given below, find its inverse and then graph both the function and its inverse.
1. \( f(x) = \sqrt{x - 2} - 2 \)
2. \( g(x) = -2x - 3 \)
3. \( f(x) = \frac{1}{2}x + 1 \)
4. \( h(x) = 2(x - 2)^3 \)
5. \( h(x) = (x + 1)^3 - 3 \)
6. \( g(x) = x + 4 \)
7. \( f(x) = \sqrt[3]{x - 1} + 1 \)
8. \( f(x) = -x - 2 \)
9. \( f(x) = (x - 2)^3 \)
10. \( f(x) = -\frac{3}{5}x + 3 \)
**Find the inverse of each function for \( x > 0 \). Then graph the function and its inverse.**
11. \( y = (x - 1)^2 - 4 \)
12. \( y = 2(x - 1)^2 + 1 \)
13. \( y = -2(x - 4)^2 - 2 \)
14. \( y = -(x - 2)^2 - 1 \)
### Explanation of Graphs and Diagrams
No graphs or diagrams are provided in the image. For each function, you will need to:
1. Solve for the inverse function \( f^{-1}(x) \) or \( y^{-1} = f^{-1}(x) \).
2. Plot the original function and its inverse function on the same coordinate plane.
3. Verify that the graphs are symmetrical with respect to the line \( y = x \), which is a characteristic feature of inverse functions.
These exercises will help in visualizing the concept of inverse functions and their graphical representation.
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