1. Inverse Relations and Functions 7-7

2. Inverse Relations If a relation maps element a of its domain to element b of its range, the INVERSE RELATION “undoes” the relation and maps b back to a. So if (a,b) is an ordered pair of a relation, then (b,a) is an ordered pair of its inverse. If a relation maps element a of its domain to element b of its range, the INVERSE RELATION “undoes” the relation and maps b back to a. So if (a,b) is an ordered pair of a relation, then (b,a) is an ordered pair of its inverse. 1.21.41.61.9121.21.41.61.912 RELATION r INVERSE OF RELATION r

3. Interchanging x and y Find the inverse of y = x 2 + 3

4. Functions and Relations Does define a function? Is its inverse a function?

5. Graphing a Relation and its Inverse The reflection over the line y = x is the graph of the inverse. You can also find points on the graph of the inverse by reversing the coordinates of the points on the relation.

6. Notation The inverse of f is denoted by f -1. Read f -1 as “the inverse of f” or as “f inverse.” The notation f(x) is used for functions, but f -1 (x) may be a relation that is not a function. If f and f -1, are functions, they are called inverse functions. For inverse functions and

7. Real Life Problems with Formulas Functions that model real-life situations are frequently expressed as formulas with letters that remind you of the variables they represent. When finding the inverse of a formula, it would be very confusing to interchange the letters. Keep the letters the same and just solve the formula for the other variable