Inverse Function
Inverse Operation:
Identity Operation:
Identity Function:
Inverse of a Function:
For any function f and its inverse f-1, the domain of f is _____________ of f-1 and the
range of f is the ________________ of f-1.
EX 1: Find the inverse of f ( x)  4 x
To verify that two functions f and g are inverses of each other,
EX 2: Verify f ( x)  2 x  3 is the inverse of g ( x) 
x3
2
Graphs inverse functions
If (a, b) lies on the graph of f, then the point ______must lie on the graph of f-1.
Graph the inverse of f (x)
6
4
fx = 2x2+4x-3
2
-5
5
-2
-4
-6
The inverse of a function is a reflection about _____________________
Horizontal Line Test:
If a function passes the horizontal line test it is said to be _________________
One-to-One Functions:
Does f have an inverse. Explain.
6
4
y=f(x)
2
-5
5
-2
-4
-6
Finding Inverses Algebraically
To find an inverse algebraically…
1.
2.
3.
4.
5.
EX 1 Find the inverse of f ( x)  4 x  5
EX 2 Find the inverse of g ( x)  4  x 2 on the interval 0  x  2.
EX 3: The per capita consumption f (in gallons) of bottled water in the United States
from 1994 through 1999 is shown in the table. The time (in years) is given by t, with t = 4
corresponding to 1994.
t
4
5
6
7
8
9
f(t)
10.7
11.6
12.5
13.1
16.0
18.1
(a) Does f--1 exist?
(b) If f--1 exist, what does it represent in the context of the problem?
(c) If f--1 exist, find f--1(16.0)
HW: page 84 problems 41, 49, 51, 61, 67, 77, 81
Homework: page 83 #’s 7, 9, 11, (13, 15, 17, 19 show graphically), 25, 29, 31