Math CentralQuandaries & Queries


Question from San, a student:

Is the inverse of a function always a function? Please justify. Thank You!

Hi San,

Suppose that you have some expression involving x and y and y is a function of x. If you substitute a value of x and solve for y you obtain at most one value of y, you never obtain two values of y. The inverse of this expression is obtained by interchanging the roles of x and y. Let's try an example.

Write the simplest polynomial y = f(x) you can think of that is not linear. This will be a function since substituting a value for x gives one value for y. Is the inverse a function? To answer this you interchange the roles of x and y, that is substitute a value for y, say y = 1, and solve for x. How many values for x did you find? If you only found one value for x try y = 0.


About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS