Part II: The Answers
136
Answers
1–100
26.
f x
x
−
= −
1
2
8
5
( )
, x ≥ 0
First replace f
 
(x) with y:
f x
x
y
x
( ) =
−
=
−
8 5
8 5
Then replace y with x and each x with y. After making the replacements, solve for y to
find the inverse:
x
y
x
y
y
x
y
x
=
−
= −
= −
= −
8 5
8 5
5
8
8
5
2
2
2
Therefore, the inverse of f x
x
( ) =
−
8 5 is
f x
x
x
−
= −
≥
1
2
8
5
0
( )
, where
The domain of the inverse is x ≥ 0 because the range of f
 
(x) is y ≥ 0 and the domain of
f x
−1 ( ) is equal to the range of f
 
(x).
27.
f x
x
−
=
−
1
5
7
3
( )
First replace f
 
(x) with y:
f x
x
y
x
( ) =
+
=
+
3
7
3
7
5
5
Then replace y with x and each x with y. After making the replacements, solve for y to
find the inverse:
x
y
x
y
x
y
x
y
=
+
− =
− =
− =
3
7
7 3
7
3
7
3
5
5
5
5
Therefore, the inverse of f
 
(x) = 3x
5
+ 7 is
f x
x
−
=
−
1
5
7
3
( )
28.
f x
x
x
x
−
= −
+
( ) − < ≤
1
2
2 2
1
1
1
( )
,
First replace f
 
(x) with y:
f x
x
x
y
x
x
( ) =
−
+
=
−
+
2
2
2
2