2Inverse RelationsTwo relations are inverses if and only if one relation contains the element (b, a) whenever the other relation contains the element (a, b).If f(x) denotes a function then f-1(x) denotes the inverse. The inverse is not necessarily a function.Inverses are symmetric to each other with respect to the line y = x.
4Horizontal line test – used to determine if the inverse of a relation will be a function. If every horizontal line intersects the graph of the relation in at most one point, then the inverse of the relation is a function.
5Finding the inverse algebraically – 1. let y = f(x) 2 Finding the inverse algebraically – 1. let y = f(x) 2. Interchange x and y 3. Solve the resulting equation for y.
6Ex 2 f(x) = x2 - 4Is the inverse a function?Find the inverse.Graph.