Question 1121070: Let A = {1,2,3,4} and B = {a,b,c,d} and let f = {(1,a),(2,a),(3,d),(4,c)}. Show that f is a function but f^-1 is not a funtion
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
A relation is NOT a function if there are two (or more) different outputs for the same input.
The given function is f: {(1,a),(2,a),(3,d),(4,c)}. The inputs are all different, so there is no possibility that there are different outputs for the same input.
Therefore f is a function.
The inverse function is f^-1: {(a,1),(a,2),(d,3),(c,4)}. Input a has two different outputs (1 and 2); therefore f^-1 is not a function.
|
|
|
