Algebra II Name _________________________________
Worksheet –Inverses of Functions/ More Domain & Range
State the inverse of each relation
1. Given the ordered pairs:
0,45,12,3
the inverse points are: _______________________________
Graph the inverse.
Is this an example of an inverse function? _______
2. Given the table:
the inverse is:
Is this an example of an inverse function? _______
3. Given the graph: the inverse is:
(it may help to list the ordered pairs….)
Is this an example of an inverse function? _______
Verify that f and g are inverse functions. Find
xgf
and
xfg
.
4.
5.
Given the following graph, determine if it is a function using the vertical line test, if the inverse is a function using
the horizontal line test, and then graph the inverse by choosing points from the graph and flipping the x and y.
6.
Function: _______ Function: ________
Original ordered pairs: _____________________
Inverse ordered pairs: _____________________
7.
Function: _______ Function: ________
Original ordered pairs: _____________________
Inverse ordered pairs: _____________________
8. How does the graph of the original function compare to the graph of the inverse?
It is a reflection over the line ________________ (fill in the equation of the line)
Given the equation of the function, write the equation of the inverse,
xg
.
9.
13)( xxf
10.
4
2
1
)( xxf
11.
3
2
)(
x
xf
12.
0;)(
2
xxxf
13.
3)(
3
xxf
14.
0;12)(
2
xxxf
Find the inverse of each function and then graph the equation and its inverse on the same coordinate plane.
15.
2)( xxf
xg
_____________
Graph of
xgandxf
(label each)
16.
12)( xxf
xg
_____________
Graph of
xgandxf
(label each)
17.
0;1)(
2
xxxf
x
y
xg
_____________
Graph of
xgandxf
(label each)
Review composite functions: If
23
2
xxgandxxf
, find
18.
5fg
19.
5gf
20.
2fg
