Wonder if there's a way using not so advanced analysis tools to prove this, and not to do it by the old way by proving first that is injective and surjective.
Show that where is a bijection. Wonder if there's a way using not so advanced analysis tools to prove this, and not to do it by the old way by proving first that is injective and surjective.
Well I'm having problems to prove surjectivity, can you help me with that?
What AsZ said is simpler, but here's another way to think of it.
Its limit at infinity is 1 and its limit at -infinity is -1. It's continuous on a connected set, so its image is connected, i.e. an interval. So its image contains (-1, 1).
What AsZ said is simpler, but here's another way to think of it.
Its limit at infinity is 1 and its limit at -infinity is -1. It's continuous on a connected set, so its image is connected, i.e. an interval. So its image contains (-1, 1).
And to prove that f is 1-1 you need to use Rolle's theorem.