sulpcegu5e ppt 5_2
TRANSCRIPT
Section 5.2
One-to-One Functions;
Inverse Functions
OBJECTIVE 1
(a)
(b) {(1,5), (2,8), (3,11), (4,14)}
Dan
John
Joe
Andy
Saturn
Pontiac
Honda
Student Car
For each function, use the graph to determine whether the function is one-to-one.
(a) (b)
A function that is increasing on an interval I is a one-to-one function in I.
A function that is decreasing on an interval I is a one-to-one function on I.
OBJECTIVE 2
Dan
John
Joe
Michelle
Saturn
Pontiac
Honda
Chrysler
Student Car
Find the inverse of the following function. Let the domain of the function represent certain students, and let the range represent the make of that student’s car. State the domain and the range of the inverse function.
{(1,5), (2,8), (3,11), (4,14)}
State the domain and the range of the function and its inverse.
3 1 3
1
1 -1
Verify that the inverse of 2 is 2
by showing that for all in the domain of
and for all in the domain of .
g x x g x x
g g x x x g
g g x x x g
1
1
1
1 1 1Verify that the inverse of is .
2 1 2 2
For what values of is ?
For what values of is ?
f x f xx x
x f f x x
x f f x x
OBJECTIVE 3
x
y
(-1,0)
(0,3)
(1,4)
The graph shown is that of a one-to-one function. Draw the graph of the inverse.
OBJECTIVE 4
-1
1Find the inverse of 1.
3
Graph and on the same coordinate axes.
f x x
f f
2 1, 1
1
xf x x
x
Find the domain and the range of
2 1
1
xf x
x
2Find the inverse of 1 if 1.y x x