Consider the function f(x) = cos(x2 - 2) + 1 on the interval (-3,3). Calculate the two x-intercepts of this function on the given interval. Express your answers in exact form, as a comma separated list. You may not use the zero/root functionality of a calculator to do this; you must show all of your work and explain your reasoning, where necessary.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Consider the function f(x) = cos(x2 – 2) + 1 on the interval (-3,3). Calculate the two x-intercepts of this function on the given interval. Express your answers in exact form, as a comma separated list. You may not use the zero/root functionality of a calculator
to do this; you must show all of your work and explain your reasoning, where necessary.
X =
Transcribed Image Text:Consider the function f(x) = cos(x2 – 2) + 1 on the interval (-3,3). Calculate the two x-intercepts of this function on the given interval. Express your answers in exact form, as a comma separated list. You may not use the zero/root functionality of a calculator to do this; you must show all of your work and explain your reasoning, where necessary. X =
Expert Solution
Step 1: For x-intercept, put f(x) = 0.

f(x)=cos(x2-2)+10=cos(x2-2)+1cos(x2-2)=-1

As we already know, the solution to the trigonometric equation cosθ=-1is:

θ=....-3π,-π,π,3π... and so on.

Therefore,

cos(x2-2)=cos(-3π)orcos(x2-2)=cos(-π)orcos(x2-2)=cos(π)orcos(x2-2)=cos(3π)..and so on

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