Final answer:
The incorrect statement about inverse functions is that the variable 'x' has the same real world meaning in both the function and its inverse. The roles of the variables are swapped when dealing with inverses, meaning the independent variable becomes dependent and vice versa.
Step-by-step explanation:
The statement that is false regarding inverse functions is: 'When someone states that y=f(x) has an inverse function y=f¹(x), the variable x in both equations has the same real world meaning.' In the context of functions and their inverses, the 'x' in the original function becomes the 'y' in the inverse function, and vice versa; meaning the roles of the independent and dependent variables are switched in the inverse.
The horizontal axis on a graph, commonly referred to as the x-axis, generally represents the independent variable, while the vertical axis, or y-axis, represents the dependent variable. A function only has an inverse if every x-value maps to a unique y-value. If a function maps two different x-values to the same y-value, it fails the Horizontal Line Test and thus does not have an inverse because the inverse would not pass the Vertical Line Test, which means for every y-value there should be exactly one x-value. This is necessary for the relationship to be a function.