Q5) Given - Let f(x) = 9x²-49 9(x) = 3x - 7 To find a) (fog) (x) b) (gof)(x) c) (f)(x) Colution = a) (fog)(x) = f(g(x)) = f[Bx-1] c) [ (fog)(x) 2. (fog) (x) = 81x² 378x + 329 b) (gof) (x) = g(F(x)) (gof) (x) = (f)(x) = 9 (3x-7) - 49 = F [9x²=42x+49]-49 81x²-378 +378 - 49 2 97x²-147-7 = 271²³-154 f(x). 9(x) 9 (9x²-49) 3 (9²-49) - 7- since g(x)=32-7 92²-49 3K-7 since g(x)= 3x-7 2 - since f(x) = 9x ² = 49 ( ) (x²) = 3x +7 I 14 T (T) (3x-7)(3x +7) [since a²_b² = (a + b) (a^b)] (3x7)

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter8: Introduction To Functions
Section8.8: Linear And Quadratic Functions
Problem 4ST
icon
Related questions
Question

TRANSCRIBE THE FOLLOWING TEXT IN DIGITAL FORMAT

2
Q5) Given let f(x) = 9x²-49
9(x) = 3x - 7
To find = a) (fog) (H)
b) (gof) (x)
e) (fox)
Solution = a) (fog)(x) = f(g(x))
b) (gof) (x) =
=
[ (fog)(x)
L
2 (fog) (H) = 81x² = 378x +329
(gof) (x)
£)(x)
=
=
=
n
=
= 9 (3x-7)- 49 - since f(x)=9x²=49
- 9 [92²-42x+49] -49
= f[3x-7] . since g(x)=38-7
2
81x²-376x +378 -49
g(f(x))
9 (9x²-49)
3 (9x²-49) -7 - since 9(x)=32-7
2
97x²-147 - 7
2
974²-154
f(x)
9(x)
9x²-49
31-7
( ) ( x ) = 3x+7
2
11
(3-7) (3x+7) [since a²_b² = (a+b)(a+b)]
(3x-7)
IT
Transcribed Image Text:2 Q5) Given let f(x) = 9x²-49 9(x) = 3x - 7 To find = a) (fog) (H) b) (gof) (x) e) (fox) Solution = a) (fog)(x) = f(g(x)) b) (gof) (x) = = [ (fog)(x) L 2 (fog) (H) = 81x² = 378x +329 (gof) (x) £)(x) = = = n = = 9 (3x-7)- 49 - since f(x)=9x²=49 - 9 [92²-42x+49] -49 = f[3x-7] . since g(x)=38-7 2 81x²-376x +378 -49 g(f(x)) 9 (9x²-49) 3 (9x²-49) -7 - since 9(x)=32-7 2 97x²-147 - 7 2 974²-154 f(x) 9(x) 9x²-49 31-7 ( ) ( x ) = 3x+7 2 11 (3-7) (3x+7) [since a²_b² = (a+b)(a+b)] (3x-7) IT
Expert Solution
steps

Step by step

Solved in 3 steps with 9 images

Blurred answer
Recommended textbooks for you
Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill