Question

Which function has an inverse that is also a function?

Answer 1

Answer:

Option (C)

Step-by-step explanation:

Option (A):

(-1, -2),(0, 4), (1, 3), (5, 14), (7, 4)

In these ordered pairs (4, 4) and (7, 4) have the same y-value.

This function is not a one-to-one function.

Therefore, this function will have no inverse function.

Option (B):

(-1, 2), (0,4), (1, 5), (5, 4), (7, 2)

(-1, 2) and (7, 2) have the same output values for input values -1 and 7.

This function is not a one-to-one function.

Therefore, this function will have no inverse function.

Option (C).

(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)

For every input value there is a different output value in these pairs.

So the function is one-to-one function.

Therefore, inverse of this function will be a function.

Option (D).

(-1, 4), (0, 4), (1, 2), (5, 3), (7, 1)

Here (-1, 4) and (0, 4) show the same y-value which shows, the given function is not a one-to-one function.

Therefore, inverse of this function will not be a function.