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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________
Function Inverses
State if the given functions are inverses.
1)
g
(
x
)
=
4 −
3
2
x
f
(
x
)
=
1
2
x +
3
2
2)
g
(
n
)
=
−12 − 2
n
3
f
(
n
)
=
−5 + 6
n
5
3)
f
(
n
)
=
−16 +
n
4
g
(
n
)
=
4
n + 16
4)
f
(
x
)
=
−
4
7
x −
16
7
g
(
x
)
=
3
2
x −
3
2
5)
f
(
n
)
=
−
(
n + 1
)
3
g
(
n
)
=
3 +
n
3
6)
f
(
n
)
=
2
(
n − 2
)
3
g
(
n
)
=
4 +
3
4
n
2
7)
f
(
x
)
=
4
−
x − 2
+ 2
h
(
x
)
=
−
1
x + 3
8)
g
(
x
)
=
−
2
x
− 1
f
(
x
)
=
−
2
x + 1
Find the inverse of each function.
9)
h
(
x
)
=
3
x − 3
10)
g
(
x
)
=
1
x
− 2
11)
h
(
x
)
=
2
x
3
+ 3
12)
g
(
x
)
=
−4
x + 1
-1-
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Worksheet by Kuta Software LLC
13)
g
(
x
)
=
7
x + 18
2
14)
f
(
x
)
=
x + 3
15)
f
(
x
)
=
−
x + 3 16)
f
(
x
)
= 4
x
Find the inverse of each function. Then graph the function and its inverse.
17)
f
(
x
)
=
−1 −
1
5
x
x
y
−6 −5 −4 −3 −2 −1 1 2 3 4 5 6
−6
−5
−4
−3
−2
−1
1
2
3
4
5
6
18)
g
(
x
)
=
1
x − 1
x
y
−6 −5 −4 −3 −2 −1 1 2 3 4 5 6
−6
−5
−4
−3
−2
−1
1
2
3
4
5
6
19)
f
(
x
)
=
−2
x
3
+ 1
x
y
−6 −5 −4 −3 −2 −1 1 2 3 4 5 6
−6
−5
−4
−3
−2
−1
1
2
3
4
5
6
20)
g
(
x
)
=
−
x − 5
3
x
y
−6 −5 −4 −3 −2 −1 1 2 3 4 5 6
−6
−5
−4
−3
−2
−1
1
2
3
4
5
6
-2-
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________
Function Inverses
State if the given functions are inverses.
1)
g
(
x
)
=
4 −
3
2
x
f
(
x
)
=
1
2
x +
3
2
No
2)
g
(
n
)
=
−12 − 2
n
3
f
(
n
)
=
−5 + 6
n
5
No
3)
f
(
n
)
=
−16 +
n
4
g
(
n
)
=
4
n + 16
Yes
4)
f
(
x
)
=
−
4
7
x −
16
7
g
(
x
)
=
3
2
x −
3
2
No
5)
f
(
n
)
=
−
(
n + 1
)
3
g
(
n
)
=
3 +
n
3
No
6)
f
(
n
)
=
2
(
n − 2
)
3
g
(
n
)
=
4 +
3
4
n
2
Yes
7)
f
(
x
)
=
4
−
x − 2
+ 2
h
(
x
)
=
−
1
x + 3
No
8)
g
(
x
)
=
−
2
x
− 1
f
(
x
)
=
−
2
x + 1
Yes
Find the inverse of each function.
9)
h
(
x
)
=
3
x − 3
h
−1
(
x
)
=
(
x + 3
)
3
10)
g
(
x
)
=
1
x
− 2
g
−1
(
x
)
=
1
x + 2
11)
h
(
x
)
=
2
x
3
+ 3
h
−1
(
x
)
=
3
x − 3
2
12)
g
(
x
)
=
−4
x + 1
g
−1
(
x
)
=
−
1
4
x +
1
4
-1-
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Worksheet by Kuta Software LLC
13)
g
(
x
)
=
7
x + 18
2
g
−1
(
x
)
=
2
x − 18
7
14)
f
(
x
)
=
x + 3
f
−1
(
x
)
=
x − 3
15)
f
(
x
)
=
−
x + 3
f
−1
(
x
)
=
−
x + 3
16)
f
(
x
)
= 4
x
f
−1
(
x
)
=
x
4
Find the inverse of each function. Then graph the function and its inverse.
17)
f
(
x
)
=
−1 −
1
5
x
x
y
−6 −5 −4 −3 −2 −1 1 2 3 4 5 6
−6
−5
−4
−3
−2
−1
1
2
3
4
5
6
f
−1
(
x
)
=
−5
x − 5
18)
g
(
x
)
=
1
x − 1
x
y
−6 −5 −4 −3 −2 −1 1 2 3 4 5 6
−6
−5
−4
−3
−2
−1
1
2
3
4
5
6
g
−1
(
x
)
=
1
x
+ 1
19)
f
(
x
)
=
−2
x
3
+ 1
x
y
−6 −5 −4 −3 −2 −1 1 2 3 4 5 6
−6
−5
−4
−3
−2
−1
1
2
3
4
5
6
f
−1
(
x
)
=
3
−
x + 1
2
20)
g
(
x
)
=
−
x − 5
3
x
y
−6 −5 −4 −3 −2 −1 1 2 3 4 5 6
−6
−5
−4
−3
−2
−1
1
2
3
4
5
6
g
−1
(
x
)
=
−3
x − 5
-2-
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