Let a,b,c E R with b != ac and let the function f : R --> R be given by
f(x) = a if x = c
f(x) = (ax - b) / (x - c) if x != c
Show that f(x) is one-to-one
Show that f(x) is onto
Show the inverse of f(x)
The Attempt at a Solution
I don't want anyone to solve this for me, i just need a push in the right direction. My textbook is next to useless. There are no similar examples showing how to work with piecewise functions.
The one thing my book shows is that we take 2 arbitrary variables and prove that f(v1) and f(v2) have differing values in the domain and range.
How can you even conclude that a function is one-to-one with such a weak proof though? Especially complex piecewise functions like mine.