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 = 1, 2, 3, 4, 5
Y = 0, 1, 0, 2, 0
no, since it is not 1-to-1
To find the inverse of the given relation, we need to swap the x and y values of each ordered pair.
Original relation:
X = 1, 2, 3, 4, 5
Y = 0, 1, 0, 2, 0
Inverse relation:
X = 0, 1, 0, 2, 0
Y = 1, 2, 3, 4, 5
Now, to determine if the inverse is a function, we need to check if each input (x-value) in the inverse relation corresponds to a unique output (y-value). If there are any repeated inputs, then the inverse is not a function.
In this case, we can see that the input 0 in the inverse relation corresponds to two different outputs: 1 and 3. Therefore, the inverse is not a function.
To find the inverse of a relation given in a table, we need to swap the x-values with the y-values to create new pairs.
The given relation is:
X = 1, 2, 3, 4, 5
Y = 0, 1, 0, 2, 0
Swapping the x and y values, we get the inverse relation:
X = 0, 1, 0, 2, 0
Y = 1, 2, 3, 4, 5
The ordered pairs for the inverse relation are:
(0, 1), (1, 2), (0, 3), (2, 4), (0, 5)
To determine if the inverse is a function, we need to check if each x-value is unique or if it repeats. If there are any repeated x-values, then the inverse relation is not a function.
Looking at the inverse ordered pairs, we notice that the x-value of 0 repeats three times. Therefore, the inverse relation is not a function since the x-value 0 has multiple corresponding y-values.
In conclusion, the ordered pairs for the inverse relation are:
(0, 1), (1, 2), (0, 3), (2, 4), (0, 5)
And the inverse relation is not a function.