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8. Graph the function and its inverse using the same set of axes (a) f(x) = 3" f(x) = log3 r 3x + 7 r +7 (b) f(r) = f-(1) = %3D 2.x – 1 2x – 3

8. Graph the function and its inverse using the same set of axes (a) f(x) = 3" f(x) = log3 r 3x + 7 r +7 (b) f(r) = f-(1) = %3D 2.x – 1 2x – 3

Algebra and Trigonometry (6th Edition)
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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**Problem 8: Graphing Functions and Their Inverses** Graph the function and its inverse using the same set of axes. **(a)** \( f(x) = 3^x \) \( f^{-1}(x) = \log_3 x \) **(b)** \( f(x) = \frac{3x + 7}{2x - 1} \) \( f^{-1}(x) = \frac{x + 7}{2x - 3} \) **Explanation for Graphs/Diagrams:** 1. **Part (a)**: - The function \( f(x) = 3^x \) is an exponential function. - Its inverse, \( f^{-1}(x) = \log_3 x \), is a logarithmic function. - When graphing both on the same set of axes, they will be reflections of each other over the line \( y = x \). 2. **Part (b)**: - The function \( f(x) = \frac{3x + 7}{2x - 1} \) is a rational function. - Its inverse, \( f^{-1}(x) = \frac{x + 7}{2x - 3} \), is also a rational function. - Both the function and its inverse will exhibit typical rational behavior such as asymptotes, and they will be reflections over the line \( y = x \). In graphing exercises, understanding the reflection property and behavior of inverse functions is crucial for accuracy.
Transcribed Image Text:**Problem 8: Graphing Functions and Their Inverses** Graph the function and its inverse using the same set of axes. **(a)** \( f(x) = 3^x \) \( f^{-1}(x) = \log_3 x \) **(b)** \( f(x) = \frac{3x + 7}{2x - 1} \) \( f^{-1}(x) = \frac{x + 7}{2x - 3} \) **Explanation for Graphs/Diagrams:** 1. **Part (a)**: - The function \( f(x) = 3^x \) is an exponential function. - Its inverse, \( f^{-1}(x) = \log_3 x \), is a logarithmic function. - When graphing both on the same set of axes, they will be reflections of each other over the line \( y = x \). 2. **Part (b)**: - The function \( f(x) = \frac{3x + 7}{2x - 1} \) is a rational function. - Its inverse, \( f^{-1}(x) = \frac{x + 7}{2x - 3} \), is also a rational function. - Both the function and its inverse will exhibit typical rational behavior such as asymptotes, and they will be reflections over the line \( y = x \). In graphing exercises, understanding the reflection property and behavior of inverse functions is crucial for accuracy.
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