00:01
This problem asks us to explain how one would go about restricting the domain of the sign function in order to produce a one -to -one function.
00:10
We know that this would be necessary because sign is a periodic function, meaning that as it approaches infinity, it continues to oscillate through the same set of values.
00:21
So if we wanted to limit it to become a one -to -one function, we would want to find a range in our domain, where our function never reproduces the same y value.
00:36
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.
00:45
Let me just mark out this space right here.
00:53
So if you look here, this from negative pi halves to pi halves, we see the sign is effectively a one -to -one function.
01:05
So this is one way that you could limit the domain of the sign function to be one to one...