The rational function $c(x) := \frac{x+1}{x-1}$ is called Cayley transformation
b) Show that $c:U\rightarrow V$ is bijective

Question

The rational function $c(x) := \frac{x+1}{x-1}$ is called Cayley transformation
b) Show that $c:U\rightarrow V$ is bijective

blockcolder · Answer

Are $U, V \subseteq \mathbb{R}$?

anonymous · Answer

hmm thats not given but above its written there rational function c(x):...
i think its U, V \subset \mathbb{R}

anonymous · Answer

also i mean we suppose yes..

anonymous · Answer

understand?

blockcolder · Answer

First show that $c(x)$ is one-to-one.
$c(x)$ is one-to-one if for all $u_1, u_2\in U, c(u_1)=c(u_2) \Rightarrow u_1=u_2$.
Then show that $c(x)$ is onto.
$c(x)$ is onto if for all $v\in V, \exists u\in U(c(u)=v)$.

anonymous · Answer

ok thank you blockfolder i have 2 more smilar question, i will post it very soon. i would be happy if you take look at it too