Inverse Functions

The definition of inverse functions.

An inverse function, of a function

, is a function such that

for all x in the domain of

and

for all y in the target of

. Informally we can think of

undoing the work that

has done. Therefore, when evaluating

, the original input, a, will be obtained. The graph below shows the functions

and the points A and B. By adjusting the values of a, you can move the points A and B.

What is the relationship between the points A and B?

Calculate for .

What happens if you plug as an input into the function for the values of in Question 2?

If for all values in the domain of evaluating gives some value , and evaluating returns , what is the relationship between the functions?

Using the graph of below, and your knowledge of inverse functions, can you estimate the values of ?