6.2 Inverse functions and Relations 1. 2 Recall that a relation is a set of ordered pairs. The inverse relation is the set of ordered pairs obtained by.

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Presentation transcript:

6.2 Inverse functions and Relations 1

2 Recall that a relation is a set of ordered pairs. The inverse relation is the set of ordered pairs obtained by exchanging the coordinates of each ordered pair. The domain of a relation becomes the range of it’s inverse The range of a relation becomes the domain of it’s inverse.

3 GEOMETRY The ordered pairs of the relation {(1, 3), (6, 3), (6, 0), (1, 0)} are the coordinates of the vertices of a rectangle. Find the inverse of this relation. Describe the graph of the inverse.

4 GEOMETRY The ordered pairs of the relation {(–3, 4), (–1, 5), (2, 3), (1, 1), (–2, 1)} are the coordinates of the vertices of a pentagon. What is the inverse of this relation?

Inverse Properties 5 As with relations, the ordered pairs of inverse functions are also related. We write the inverse of the function f(x) as f -1 (x)

Graphs of inverses When the inverse of a function is also a function, the original function is one–to–one. Since we use a vertical line test to determine if a relation is a function, we can use a horizontal line test to determine whether the inverse is also a function. 6

To find an inverse 7

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Two Functions are inverses of each other if… Both f(g(x)) = x and g(f(x)) = x 10

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