Question

A relation is given in the table below write out the ordered pairs for the inverse and then determine if the inverse is a function

x y
1 0
2 1
3 0
4 2
5 0

a) (1,0), (2,1), (3,0), (4,2), (5,0) inverse is not a function
b) (0,1), (1,2), (0,3), (2,4), (0,5) inverse is not a function
c) (0,1), (1,2), (2,4) inverse is a function
d) (0,1), (1,2), (0,3), (2,4), (0,5) inverse is a function

Answer 1

B, the inverse is not a function, because to the x-value 0 the inverse relation orders two values: the 1 and the 5 as well.

Answer 2

Option b is correct.

{(0,1), (1,2), (0,3), (2,4), (0,5)} inverse is not a function

Explanation:

Inverse function states that the set of all ordered pairs obtained by interchanging the first and second elements of each ordered pair in the original function.

As per the statement:

A relation is given in table:

x y

1 0

2 1

3 0

4 2

5 0

We an write this as:

{(1,0), (2,1), (3,0), (4,2), (5,0)}

by definition of inverse function;

{(0,1), (1,2), (0,3), (2,4), (0,5)}

A function is a relation in which each input has a unique output value.

Since, this inverse is not a function because the input value of 0 does not have unique output.

⇒{(0,1), (1,2), (0,3), (2,4), (0,5)} inverse is not a function