Operations for functions: Inverse functions
Characterizing invertible functions
The function #f# with domain #\{1,2,3,4,5\}# is described by \[f=[3,4,5,2,1]\] The meaning of the notation is as follows: for every #j\in\{1,2,3,4,5\}#, the value #f(j) # is equal to the value at position #j# in this list. For example #f(2)# is equal to the value at the second position, hence #f(2) = 4#.
Because all five values of #f# differ, this function is injective, and hence invertible. What is the inverse of #f#?
Describe #f^{-1}# by a list of five numbers as was done for #f#.
Because all five values of #f# differ, this function is injective, and hence invertible. What is the inverse of #f#?
Describe #f^{-1}# by a list of five numbers as was done for #f#.
| #f^{-1}=# |
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