18.
710711
Find the inverse of each one-to-one function. Graph the function and its inverse on one coordinate plane.
19.
J
= {(8, 2), (1, 1), (0, 0), (
−
8,
−
2)}
20.
K
= {(
−
7, 1), (6, 2), (3,
−
1), (2, 5)}
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Find the inverse of each function.
21.
f
(
x
) = 4
x
−
5
22.
f
(
x
) = 8
−
3
x
23.
f
(
x
) =
x
3 + 7
24.
f
(
x
) = 3
−
x
3
25.
f open parenthesis x close parenthesis equals
−
4 over x
26.
f open parenthesis x close parenthesis equals 3 over x
27.
f open parenthesis x close parenthesis equals 4 over begin denominator x
−
5 end denominator
28.
f open parenthesis x close parenthesis equals 2 over begin denominator 3 plus x end denominator
For the given function f and its inverse, find f
[
f
−
1
(
x
)]
.
29.
f open parenthesis x close parenthesis equals begin numerator x
−
3 end numerator over 5 semicolon f to the
−
1 open parenthesis x close parenthesis equals 5 x plus 3 power
30.
f open parenthesis x close parenthesis equals x over 2 plus 1 semicolon f to the
−
1 open parenthesis x close parenthesis power equals 2 x
−
2
Find the inverse of each function. Graph the function and its inverse on one coordinate plane. Graph the line y
=
x as a dashed line.
31.
g
(
x
) = 2
x
+ 5
32.
f
(
x
) = 3
x
+ 4
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33.
h open parenthesis x close parenthesis equals 1 over 2 x
−
2
34.
p open parenthesis x close parenthesis equals 2 over 3 x
−
4
35.
r
(
x
) =
−
3
x
−
1
36.
k
(
x
) = 3
−
2
x
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711712
To Think About
37.
Can you find an inverse function for the function
f
(
x
) = 2
x
2
+ 3? Why or why not?
38.
Can you find an inverse function for the function
f
(
x
) = | 3
x
+ 4| ? Why or why not?
For every function f and its inverse, f
−
1
it is true that f
[
f
−
1
(
x
)] =
x and f
−
1
[
f
(
x
)] =
x
.
Show that this is true for each pair of inverse functions.
39.
f open parenthesis x close parenthesis equals 2 x plus 3 over 2 to the comma power f to the
−
1 open parenthesis x close parenthesis power equals 1 over 2 x
−
3 over 4
40.

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