Given:
Different functions in the ordered pairs.
To find:
The function which has an inverse that is also a function.
Solution:
A relation is a function, if there exist unique output for each input.
The inverse of a function is a function, if there exist unique input for each output in the function.
It means, the inverse of a function is a function if each y value has unique x-value.
In {(-1, -2), (0, 4), (1, 3), (5, 14), (7,4)},
For y=4 we have x=0 and x=7, therefore, the inverse of this function is not a function.
In {(-1, 2), (0, 4), (1, 5), (5, 4), (7, 2)}
,
For y=4 we have x=0 and x=5, therefore, the inverse of this function is not a function.
In {(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)}
,
For all y value we have unique x values, therefore, the inverse of this function is a function.
In {(-1, 4), (0, 4), (1, 2), (5, 3), (7, 1)},
For y=4 we have x=-1 and x=0, therefore, the inverse of this function is not a function.
Therefore, the correct option is C.
