1.6 inverse functions
TRANSCRIPT
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