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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 or , 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.

Question 1

What is the relationship between the points A and B?

Question 2

Calculate for .

Question 3

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?

Question 4

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