Finding the Inverse of a Function Defined by a Set of Ordered Pairs

Find the inverse of the one-to-one function: \[ \{(-3,-5), (-1,1), (0,2), (1,3)\} \]

State the domain and the range of the function and its inverse.

Solution The inverse of the function is found by interchanging the entries in each ordered pair. The inverse is \[ \{(-5,-3), (1,-1), (2,0), ( 3,1)\} \]

The domain of the function is \(\{-3, -1,0, 1\}\); the range of the function is \(\{-5, 1,2,3\}\). The domain of the inverse function is \(\{-5, 1,2,3\}\); the range of the inverse function is \(\{ -3, -1,0,1\}\).