Question

Find the inverse of each function that is one-to-one. {(1, -3), (2, -7), (4, -3), (5, -5)}

Accepted Answer

First, understand that the inverse of a function swaps the roles of inputs and outputs. For a function given as a set of points, the inverse will have each ordered pair reversed, meaning the x- and y-values switch places. Check if the function is one-to-one by verifying that each output value (y-value) is unique. If any y-value repeats, the function is not one-to-one and does not have an inverse function. Since the function is given as the set {(1, -3), (2, -7), (4, -3), (5, -5)}, observe that the output -3 appears twice (for inputs 1 and 4), so the function is not one-to-one and does not have an inverse function over the entire domain. If you were to find the inverse for a one-to-one function, you would create a new set of ordered pairs by swapping each (x, y) to (y, x). For example, if the function had pairs (a, b), the inverse would have pairs (b, a). In summary, since the function is not one-to-one, it does not have an inverse function. However, if restricted to a domain where outputs are unique, you could find the inverse by swapping coordinates as described.

Find the inverse of each function that is one-to-one. {(1, -3), (2, -7), (4, -3), (5, -5)}

Verified video answer for a similar problem:

Key Concepts

One-to-One Functions

Inverse Functions

Function Representation Using Ordered Pairs