Download Inverse Function

Inverse of a Function
Recall: For each element in the domain of a function, there is exactly one element in the range.
New: The inverse of a relation can be found by interchanging the domain and the range of the relation.
Note:
f
1

1
f
1.
Find the inverse of each relation below:
a)
f (x)  {(2,3), (-4, 5), (1,4)}
f
D :
D :
R :
R :
f ( x)  3 x  1
f
b)
1
1
( x)
( x)
D :
R :
D :
R :
c)
f ( x)  x 2  2
f
1
( x)
D :
R :
Steps:
1. replace f (x ) with y
D :
2. interchange x and y
3. solve for y
R :
4. replace y with
f
1
( x)
2.
a) Graph both
f x  and f
1
x  from 1c on the grid
provided.
b) Is the inverse a function? _______________
c) How can we restrict the domain of f (x ) so that its
inverse is a function?


d) What do you notice about f (x ) and it’s inverse? _________________________________________
3. Find the inverse of each function below. If necessary, restrict the domain of the function so that the inverse is
also a function.
a)
f ( x)  2 x  3
b)
f ( x) 
x
f ( x) 
x3
4
c)
d)
f ( x)  x 2  1
e)
f ( x)  2 x  3  4
f)
f ( x) 
x 1
x5