Non-bijective functions and inverses
Think about the following statement: "The inverse of every function f can be found by reflecting the graph of f in the line y=x", is it true or false? Perhaps think about the graph of , is the reflection the graph of a function? Explain why or why not.
As seen in the previous graph, functions that are not 1-1(or injective) cannot be inverted. By reflecting about the y=x line the resulting curve was not the graph of a function. What changes are necessary to make , a bijection(one-to-one and onto)? On the next graph you can change the values of corresponding to the values of the domain [D, ) of g to change the domain of . For what intervals does have an inverse?