How do you evaluate a composite function (f ° g )(x)? Demonstrate with an example of your own or from the text. Explain the concept of inverse of a function y = f(x). Does every function have an inverse? What is the test for determining if a function has an inverse?
What Steve said is spot on. In addition to the horizontal line test there is an algebraic way to determine one to one
You start by assuming 2 arbitrary range values are equal, if we show that their corresponding domain values are equal then we get that the function is one to one.
In others words if a and b were elements in the domain of a function f then we assume f(a) = f(b) and if we arrive at a = b then the function is one to one.
ex. determine if f(x) = x3 + 2 is one to one.
Start with 2 domain elements a and b then f(a) = a3 + 3 and f(b) = b3 + 3
Then f(a) = f(b) becomes a3 + 3 = b3 + 3. After doing a little bit of algebra you will get that a = b so f(x) is indeed one to one.
This method is helpful if don't know what a graph looks like. If you know what the graph looks like then by all means go with the horizontal line test.