To show whether a function is one to one, we can use the theorem as follows
let f(x) be the one to one function
if so,
f(x1) = f(x2)
x1 = x2
When you are asked to find the range of such a rational function where you get a quadratic for the range, you can get the discriminant of that as >= 0 (as this should have real roots) and find the solutions that way.
