Precalculus Mathematics for Calculus International Metric Edition 7th Edition Stewart Solutions Manual Full download at: http://testbanklive.com/download/precalculus-mathematics-for-calculus-international-metricedition-7th-edition-stewart-solutions-manual/
2
FUNCTIONS
2.1
FUNCTIONS
1. If f x x 3 1, then (a) the value of f at x (b) the value of f at x
1 is f
13
1 23
2 is f 2
1
1
0.
9.
(c) the net change in the value of f between x
1 and x
2 is f 2
f
1
9
0
9.
2. For a function f , the set of all possible inputs is called the domain of f , and the set of all possible outputs is called the range of f . x2 T x
3. (a) f x h x
52
(b) f 5
x
3x and g x
5
have 5 in their domain because they are defined when x 5. However, T T 10 5 because 5, so 5 is not in the domain of h. 5 5 5 0 10 and g 5 0. 5 5
x 10 is undefined when x
3 5
25
15
4. (a) Verbal: “Subtract 4, then square and add 3.� (b) Numerical: x
f x
0
19
2
7
4
3
6
7
5. A function f is a rule that assigns to each element x in a set A exactly one element called f x in a set B. Table (i) defines y as a function of x , but table (ii) does not, because f 1 is not uniquely defined. 6. (a) Yes, it is possible that f 1
f 2
(b) No, it is not possible to have f 1 value of f x .
5. [For instance, let f x 5 and f 1
7. Multiplying x by 3 gives 3x , then subtracting 5 gives f x 8. Squaring x gives x 2 , then adding two gives f x 9. Subtracting 1 gives x 10. Adding 1 gives x
x2
1, then squaring gives f x
1, taking the square root gives
T
5 for all x .]
6. A function assigns each value of x in its domain exactly one
3x
5.
2. x
1 2. T
x
1, then dividing by 6 gives f x x
11. f x
2x
3: Multiply by 2, then add 3.
12. g x
2
x 1 . 6