Trigonometry

Chapter 1 Section 7

Inverse Functions

1.7 Inverse Functions

Domain Range

Student Age

Matt 15

Abbey 16

Cody 17

Miranda 15

R = {(Matt,15), (Abbey,16), (Cody,17), (Miranda,15)}

Is this relation a function?

1.7 Inverse FunctionsInverse of the relation is

Domain Range

Student Age

15 Matt

16 Abbey

17 Cody

15 Miranda

R = { (15, Matt), (16, Abbey), (17, Cody), (15, Miranda) }

Is this relation a function?

1.7 One to One FunctionsGiven this relation

{ (1,2), (3,5), (6,8), (7,9) }

Is this relation a function?

The inverse of the function is

{ (2,1), (5,3), (8,6), (9,7) }

Is this relation a function?

One to One Functions – If the inverse of a function is also a function, then the function is a one to one function.

1.7 Horizontal Line Test

Horizontal Line Test – a function is one to one if every horizontal line intersects the graph of the function in at most one point.

Increasing functions are one to one Decreasing functions are one to one

The Inverse of a function is denoted by 1( )f x−

1.7 One to one functions

If the inverse of a function is also a function, then the function is a one to one function.

If a function is one to one, then its inverse is also a function.

The graph of a function f and its inverse

are symmetrical to y=x (Identity Function)

1( )f x−

1.7 Composition of functions To show that a function f and its inverse f-1

are truly inverses, compositions must = x.

f -1 ( f (x) ) = x f (f -1 (x) ) = x