Question

Which function has an inverse that is also a function?

{(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)}
{(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)}
{(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)}
{(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}

Answer 1

The function {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)} has an inverse that is also a function.

Step-by-step explanation:

An inverse function is a function that 'undoes' the original function. For a function to have an inverse that is also a function, each input value must have a unique output value. Only one of the given options satisfies this condition.

The function {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)} has an inverse that is also a function because each input value (x-value) is paired with a unique output value (y-value).

Therefore, the correct option is {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)}.

Answer 2

Inverse of the function A is not a function because we will have pairs: ( 4, 0 ) and ( 4 , 7 ). Also for the function B : ( 4, 0 ) and ( 4, 5 ). And for D : ( 4, - 1 ), ( 4, 0 ). We must have 1 value of x for 1 value of y. So an inverse that is also a function is just C.

Answer: C ) { ( - 1 , 3 ) , ( 0 , 4 ), ( 1, 14 ) , ( 5 , 6 ), ( 7 , 2 )}