51. f(x) = x² + 5x - 16, g(x) = x³ + x²; x = 3

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Solve the problem 51 on the attached document and show your work
Performing Function Operations (pp. 279-284) WATCH
Learning Target: Perform arithmetic operations on two functions.
Find (f+g)(x) and (f- g)(x) and state the domain of each. Then evaluate f + g and
f-g for the given value of x.
48. f(x) = 3(5), g(x) = -8(5x); x = 4
5.6
Find (fg)(x) and
given value of x.
50. f(x) = 2x4+3, g(x) = x -2; x = -1 51. f(x) = x² + 5x - 16, g(x) = x³ + x²; x = 3
Determine whether the statement is always, sometimes, or never true. Explain your reasoning.
52. For two quadratic functions f and g, f + g is also a quadratic function.
53. For two functions f and g, when f(a) = 3 and g(a) = 4, (fg)(a) = 12.
5.7
49. f(x) = 3x² + 1, g(x) = x + 4; x = -5
(x) and state the domain of each. Then evaluate fg and I for the
g
WATCH
Composition of Functions (pp. 285-290)
Learning Target: Evaluate and find compositions of functions.
Use the functions f(x)=x²-3, g(x) = x + 6, and h(x) = -
the table.
x-3
2
54.
X
5
7
9
11
13
61.
g(h(x))
55.
X
-6
-4
-2
0
2
to complete
f(g(x))
Find (a) f(g(x)), (b) g(f(x)), and (c) f(f(x)). State the domain and range of each composition.
56. f(x) = 3x², g(x) = -x - 2
57. f(x) = 6x + 5, g(x) = √x + 4
58. f(x) = -7x + 1, g(x)=√x - 2
59. f(x)=x-9, g(x) = x³ - 4x + 3
60. Let f(x) = 4x - 3, g(x) = -x² + 8, and h(x) = -x. Find (a) g(h(x)),
(b) f(g(h(x))), and (c) f(g(h(4))). What do you notice about g(h(x))?
Let fhe a radical function and let a ho o lingor function with
Vocabulary
composition
Transcribed Image Text:Performing Function Operations (pp. 279-284) WATCH Learning Target: Perform arithmetic operations on two functions. Find (f+g)(x) and (f- g)(x) and state the domain of each. Then evaluate f + g and f-g for the given value of x. 48. f(x) = 3(5), g(x) = -8(5x); x = 4 5.6 Find (fg)(x) and given value of x. 50. f(x) = 2x4+3, g(x) = x -2; x = -1 51. f(x) = x² + 5x - 16, g(x) = x³ + x²; x = 3 Determine whether the statement is always, sometimes, or never true. Explain your reasoning. 52. For two quadratic functions f and g, f + g is also a quadratic function. 53. For two functions f and g, when f(a) = 3 and g(a) = 4, (fg)(a) = 12. 5.7 49. f(x) = 3x² + 1, g(x) = x + 4; x = -5 (x) and state the domain of each. Then evaluate fg and I for the g WATCH Composition of Functions (pp. 285-290) Learning Target: Evaluate and find compositions of functions. Use the functions f(x)=x²-3, g(x) = x + 6, and h(x) = - the table. x-3 2 54. X 5 7 9 11 13 61. g(h(x)) 55. X -6 -4 -2 0 2 to complete f(g(x)) Find (a) f(g(x)), (b) g(f(x)), and (c) f(f(x)). State the domain and range of each composition. 56. f(x) = 3x², g(x) = -x - 2 57. f(x) = 6x + 5, g(x) = √x + 4 58. f(x) = -7x + 1, g(x)=√x - 2 59. f(x)=x-9, g(x) = x³ - 4x + 3 60. Let f(x) = 4x - 3, g(x) = -x² + 8, and h(x) = -x. Find (a) g(h(x)), (b) f(g(h(x))), and (c) f(g(h(4))). What do you notice about g(h(x))? Let fhe a radical function and let a ho o lingor function with Vocabulary composition
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