Why don’t we consider -4/sqrt(3) <x< 0 here? Thank you!
Good question!
For the contraction property, indeed g satisfies it for -4/sqrt(3) <x< 0.
But because we want g to have a unique fixed point and the theorem requests not just contraction, but also self-mapping, we cannot consider that negative part. (It is clear that much of the images are in the positive part.) This note may be good to add for future students!
1 Like
Sorry, what do you mean by “(It is clear that much of the images are in the positive part.)”?
If you take g(x) for -4/sqrt(3) <x< 0,
you will see that most values are positive.
So you certainly do not have the self-mapping property.