Answers and Explanations 133
Answers
1–100
19.
4
3
3
8
4
5
12
x y z
Recall that x
x
m n
m
n
=
. The expression becomes
4
4
1 3 3 8 1 4 5 12
3
3
8
4
5
12
x y z
x y z
=
20.
4
1 3 2 3 1 3 4 5
x y z
Recall that x
x
m
n
m n
=
. Therefore, the expression becomes
4
4
4
2
3
4
5
2
1 3
4 5
1 3 2 3 1 3 4 5
x y z
x y
z
x y z
= ( )
=
21.
y = 3x + 8
Recall that a function is one-to-one if it satisfies the requirement that if x 1 ≠ x 2 , then
f
 
(x 1 ) ≠ f
 
(x 2 ); that is, no two x coordinates have the same y value. If you consider the
graph of such a function, no horizontal line would cross the graph in more than one
place.
Of the given functions, only the linear function y = 3x + 8 passes the horizontal line test.
This function is therefore one-to-one and has an inverse.