Find the inverse of the function and state its domain and range .
-{(-3, 4), (-1, 5), (0, 2), (2, 6), (5, 7)}
A){(4, -3), (5, -1), (2, 0), (6, 2), (7, 5)} D = {2, 4, 5, 6, 7}; R = {-3, -1, 0, 2, 5}
B){(3, 4), (1, 5), (0, 2), (-2, 6), (-5, 7)}; D = {3, 1, 0, -2, -5}; R = {2, 4, 5, 6, 7}
C){(-3, -4), (-1, -5), (0, -2), (2, -6), (5, -7)}; D = {-3, -1, 0, 2, 5}; R = {-7, -6, -5, -4, -2}
D){(3, -4), (1, -5), (0, -2), (-2, -6), (-5, -7)}; D = {3, 1, 0, -2, -5}; R = {-7, -6, -5, -4, -2}

Question

Quizplus · Accepted Answer

The given function is not one-to-one, so it doesn't have an inverse function. However, if we consider the function restricted to its range, which is {2, 5, 4, 6, 7}, then it becomes one-to-one and we can find its inverse by simply swapping the x and y values of the original function. This gives us the inverse {(4, -3), (5, -1), (2, 0), (6, 2), (7, 5)} with domain D = {2, 4, 5, 6, 7} and range R = {-3, -1, 0, 2, 5}. Therefore, the correct choice is A. The given set of points represent a function as each input has a unique output. To find the inverse, we need to switch the input and output in each point. The resulting set of points will represent the inverse function. So the inverse function of the given function is {(4, -3), (5, -1), (2, 0), (6, 2), (7, 5)}. The domain of the inverse function is the range of the given function, which is {-3, -1, 0, 2, 5}. The range of the inverse function is the domain of the given function, which is {2, 4, 5, 6, 7}. Option A matches this result.

Find the Inverse of the Function and State Its Domain