- #1
iloveannaw
- 45
- 0
Homework Statement
Given the function
[tex]f(x) = \frac{ax+b}{cx+d}[/tex]
where [tex]f: \mathbb{R} \backslash \left\{ \frac{-d}{c} \right\} \rightarrow \mathbb{R} [/tex]
show that f is either a constant or has an inverse function.
I can see why this would be true. If a function takes all real numbers and returns all real numbers then it could either be a multiplying constant or have an inverse, e.g. x2
wouldn't work here because it only returns values greater than zero.
My question is is there a theorem or lemma or something that can help me prove this?
thanks