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University of Southern California

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Problem 70

Restricted Domain Explain how to restrict the domain of the sine function so that it becomes a one-to-one function.

Answer

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## Discussion

## Video Transcript

thiss problem asks us to explain how one would go about restricting the domain of the sine function. In order to produce a 1 1 to 1 function, we know that this would be necessary because sign is a periodic function meaning that as it approaches infinity it continues to Aasa late through the same set of values. So if we wanted to limit it toe become a wonder one function we would want to find arranged in our domain, where our function never reproduces the same. Why value So looking at it, where do you think you see that? Well, a commonplace would be from the bottom of one of these troughs to the top of one of these peaks. Let me just mark out this space right here. So if you look here, this from negative pie halfs to perhaps we see the sign is effectively a 1 to 1 function s o. This is one way that you could limit the domain of the sine function to be 1 to 1 in the range. Negative halfs to pi house. And you could do this for many other places, primarily in the ranges from these peaks to these troughs so you could do from pi halfs to three pie halfs over here. Any multiple therein, you wouldn't want to do from zero to pie, for instance, because you see, and on either side of this hill we have the same value. And inside the range sign would not be 1 to 1. Because for two different X values, we find that we have the same. Why value? So you're better off limiting your domain negative pie halfs to perhaps

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