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? [br]Perhaps think about the graph of [math]f(x)=x^2[/math], 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 [math]x^2[/math] about the y=x line the resulting curve was not the graph of a function. What changes are necessary to make [math]f:R\longrightarrow R[/math], [math]f\left(x\right)=x^2[/math] a bijection(one-to-one and onto)?[br][br]On the next graph you can change the values of [math]D[/math] corresponding to the values of the domain [D, [math]\infty[/math]) of g to change the domain of [math]g(x)[/math]. For what intervals does [math]g(x)[/math] have an inverse?