Inverse Functions


The definition of inverse functions.

An inverse function, of a function , is a function such that and for all x in the domain of . In other words, given a function f(x), which has some operations(squaring, multiplying, adding..), the inverse function will perform the opposite operations of the original function(square root, dividing, subtracting...). Informally we can think of undoing the work that has done. Therefore, when evaluating or , the original value, x, 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. Q1) Is there any relationship between the points? Q2) Calculate for . Q3) What happens if you plug into the function for the values of in Q2?
Generalising, if for all values in the domain of evaluating gives some value , and evaluating returns , what is the relationship between the functions? Q4) Using the graph of , and your knowledge of inverse functions, can you estimate the values of ? What about ?