Did I do this right?
Problem:
If the following defines a one-to-one function, find its inverse. If no, write "Not one-to-one."
{(-2,4),(-1,4),(0,1),(1,-5)}
answer: Not one-to-one because of
(-2,4), (-1,4)
There is only one y for each x, so the original is indeed a function.
However the inverse has those two values of y for x is 4 so the inverse is indeed not a function.
To determine if the given function is one-to-one, we need to check if each input (x-value) corresponds to a unique output (y-value). If any two different x-values have the same y-value, then the function is not one-to-one.
Let's check the given function:
{(-2,4), (-1,4), (0,1), (1,-5)}
We can observe that the inputs -2 and -1 both have the same output value, 4. Since two different inputs have the same output, this function is not one-to-one.
Therefore, the answer is "Not one-to-one."
To determine if the function is one-to-one, we need to check if each input (x-value) corresponds to a unique output (y-value). If there are any repeated y-values for different x-values, then the function is not one-to-one.
In this case, we can see that for the x-values of -2 and -1, the outputs are both 4. Therefore, the function is not one-to-one.
To find the inverse of a function, we need to swap the x and y values. However, since this function is not one-to-one, it does not have an inverse. The concept of an inverse applies only to one-to-one functions.
Therefore, the answer is: Not one-to-one.