Explore the relationship between a function and its inverse function in this activity.
[i]Answer these open ended questions on your own or with others to form deeper math connections.[/i]
What similarities and differences do you notice between the original function and the inverse?
Explain the relationship that the graph of the function and the inverse have with the line [math]y=x[/math].
The graph of a linear function [math]f\left(x\right)[/math] passes through [math]\left(1,2\right)[/math] and [math]\left(5,1\right)[/math]. The graph of another linear function [math]g\left(x\right)[/math] passes through [math]\left(2,1\right)[/math]and [math]\left(1,5\right)[/math]. [br]Do you have enough information to say that [math]f[/math] and [math]g[/math] are inverses of each other?[br]
Could you determine if two functions are inverses if you were given only the first point for each function?
Does [math]f\left(x\right)=\left|x\right|[/math] have an inverse function?[br]What about if the domain was restricted?
What is an example of a function without an inverse?