Pre-Calculus - Section 4.5INVERSE FUNCTIONS

Describe the meaning of the word “inverse” to you. In addition, provide one example.

Describe the meaning of the phrase “composition of functions” to you. In addition, provide one example. (HINT: Remember Alg.2? ()

WARM-UP

When is f a function? When each input goes to exactly 1 output

Determine if the following are functions

REVIEW: FUNCTIONS

x y1 62 63 64 65 6

x y1 22 33 44 52 16

Inverse functions “undo” each other.

WHAT IS AN INVERSE REALLY?

Domain RangeFunction

Range DomainInverse

WE USES THE CONCEPT OF INVERSE FUNCTIONS ALL OF THE

TIME. For example, someone give us directions to their

house. Turn right, go three blocks, turn left, go one block, and turn left again.

We would use the inverse to go home.

Come up with another example of inverse functions in every day life.

HOW TO FIND AN INVERSE GIVEN POINTS

x f(x)12459

36121527

x f-1(x)12459

36121527

Graph for Graph for the same domain

EXAMPLE 1

Horizontal Line Test: If one output from the original function goes to

multiple inputs, then what will happen when with the inverse?

Determine if the inverse will be a function:

WHEN IS THE INVERSE A FUNCTION?

Given f(x):Replace with ySwitch the x’s with y’sSwitch the y’s with x’sSolve for yReplace y with

HOW TO CREATE AN INVERSE

Find the inverse of

EXAMPLE 2

YOU TRY.Find the inverse function:

3 4h( )5xx

2( ) 3 4p x x

Show that and g are inverses of each other.

EXAMPLE 3

Functions f and g are inverse if g(f(x)) = x and f(g(x)) = x for all x in either

domain.

COMPOSITION

Show that and g are inverses of each other.

EXAMPLE 3

Textbook: p.149 #7-15, 20***rule = equation of the inverse

HOMEWORK