For Exercises 59–64, (See Example 9) a. Determine if the upper bound theorem identifies the given number as an upper bound for the real zeros of f ( x ) . b. Determine if the lower bound theorem identifies the given number as a lower bound for the real zeros of f ( x ) . f ( x ) = 6 x 3 − x 2 − 57 x + 70 a. 4 b. − 4
For Exercises 59–64, (See Example 9) a. Determine if the upper bound theorem identifies the given number as an upper bound for the real zeros of f ( x ) . b. Determine if the lower bound theorem identifies the given number as a lower bound for the real zeros of f ( x ) . f ( x ) = 6 x 3 − x 2 − 57 x + 70 a. 4 b. − 4
Solution Summary: The author calculates whether 4 is an upper bound for the real zeros of f(x)=6x
Suppose f and g are the piecewise-defined functions defined
here. For each combination of functions in Exercises 51–56,
(a) find its values at x = -1, x = 0, x = 1, x = 2, and x = 3,
(b) sketch its graph, and (c) write the combination as a
piecewise-defined function.
f(x) = {
(2x + 1, ifx 0
g(x) = {
-x, if x 2
8(4):
51. (f+g)(x)
52. 3f(x)
53. (gof)(x)
56. g(3x)
54. f(x) – 1
55. f(x – 1)
In Exercises 27–28, let f and g be defined by the following table:
f(x)
g(x)
-2
-1
3
4
-1
1
1
-4
-3
-6
27. Find Vf(-1) – f(0) – [g(2)]² + f(-2) ÷ g(2) ·g(-1).
28. Find |f(1) – f0)| – [g(1)] + g(1) ÷ f(-1)· g(2).
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