Exercise Set 3.7: Inverse Functions
x
y
x
y
x
y
x
y
x
y
x
y
Determine whether each of the following graphs
represents a one-to-one function. Explain your answer.
1.
2.
3.
4.
5.
6.
Determine whether each of the following functions is
one-to-one. (Hint: First sketch a graph.)
7. 32)( −= xxf
8. 5)( 2+= xxg
9. 3
)2()( −= xxh
10. 2)( 3−= xxf
11. 4)( += xxg
12. 3
1
)( −= x
xh
13. 1)2()( 2+−−= xxf
14. 6)( −= xxg
Answer the following.
15. If a function f is one-to-one, then the inverse
function, 1−
f, can be graphed by either of the
following methods:
(a) Interchange the ____ and ____ values.
(b) Reflect the graph of f over the line
.
_
___
=
y
16. The domain of f is equal to the __________ of
1−
f, and the range of f is equal to the
__________ of .
1−
f
A table of values for a one-to-one function )(xfy
=
is
given. Complete the table for
()
xfy 1−
=.
17.
18.
x )(xf
3 -4
2 7
-4 5
5 0
0 3
x )(
1xf −
-4
2
5
0
x )(xf
5 9
4 5
6 -3
-8 2
2 6
x )(
1xf −
5
5
6
-8
