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