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Sketch the graphs of the two functions f : [0, π] → R, g : [0, π] → R where f(x) = sin(3x), and g(x) = 5 − 4 sin(3x). Explain carefully how you obtained the graph y = g(x) from the graph of y = f(x). (a) Write down the ranges of both f and g. (b) Is f one-one on this domain? Justify your answer. (c) Indicate an interval on the x–axis where f has an inverse. Justify your answer. (You have not been asked to find this inverse.)

Sketch the graphs of the two functions f : [0, π] → R, g : [0, π] → R where f(x) = sin(3x), and g(x) = 5 − 4 sin(3x). Explain carefully how you obtained the graph y = g(x) from the graph of y = f(x). (a) Write down the ranges of both f and g. (b) Is f one-one on this domain? Justify your answer. (c) Indicate an interval on the x–axis where f has an inverse. Justify your answer. (You have not been asked to find this inverse.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 59E
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1. Sketch the graphs of the two functions f : [0, π] → R, g : [0, π] → R where f(x) = sin(3x), and g(x) = 5 − 4 sin(3x). Explain carefully how you obtained the graph y = g(x) from the graph of y = f(x).

(a) Write down the ranges of both f and g.

(b) Is f one-one on this domain? Justify your answer.

(c) Indicate an interval on the x–axis where f has an inverse. Justify your answer. (You have not been asked to find this inverse.)

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