Let A = {1, 2, 3, 4, 5}. Find the inverse of the following functions f:...

Let A = {1, 2, 3, 4, 5}. Find the inverse of the following functions f: A→ A.

1. ? = {(1,1),(2,3),(3,2),(4,4),(5,5)
1. ? = {(1,5),(2,4),(3,2),(4,1),(5, 4)}
1. ? = {(2,1),(3,4),(1,3),(4,1),(5, 2)}

Expert Solution

in a function that associates to every element of the first set exactly one element in the second set.if (x,y) is in f then (y,x) is in f^-1.

In (b) when we consider the ordered pairs of f^-1, the element 4 maps to both 2 and 5,so f^-1 is not a function.so f^-1 does not exist.

In (c) f^-1 has a ordered pairs (1,2) and (1,4) so it is not a function .so f^-1 does not exist.

Inverse function is a function by definition.

Colby Messinger answered 1 day ago

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