Q. 447 For the functions, f(x) = 6x + 1... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 10: Q. 447 (page 1066)

For the functions, f(x) = 6x + 1 and
g(x) = 8x 鈭� 3, find:
$(a) (f 鈭� g) (x) (b) (g 鈭� f) (x) (c) (f 路 g) (x)$

Short Answer

Expert verified

$(a) (f 鈭� g) (x) = 48 x - 17 (b) (g 鈭� f) (x) = 48 x + 5 (c) (f 路 g) (x) = 48 x^{2} - 10 x - 3$

Step by step solution

Part (a) Step 1. Given information

Given function

f (x) = 6 x + 1 g (x) = 8 x - 3

Part (a) Step 2. Calculation

$f (x) = 6 x + 1 g (x) = 8 x - 3 N o w, s u b s t i t u t e g (x) = 8 x - 3 i n f (g (x)) f (g (x)) = f (8 x - 3) E v a l u a t i n g f (8 x - 3) r e p l a c e x b y 8 x - 3 i n f u n c t i o n f (x) = 6 x + 1 f (8 x - 3) = 6 (8 x - 3) + 1 = 48 x - 18 + 1 = 48 x - 17 (f 鈭� g) (x) = 48 x - 17$

Part (b) Step 2. Given information

$f (x) = 6 x + 1 g (x) = 8 x - 3$

Part (b) Step 2. Calculation

$(g 鈭� f) (x) = g (f (x)) N o w s u b s t i t u t e f (x) = 6 x + 1 i n g (f (x)) g (f (x)) = g (6 x + 1) T o e v a l u a t e g (6 x + 1) r e p l a c e x b y 6 x + 1 f u n c t i o n g (x) = 8 x - 3 g (6 x + 1) = 8 (6 x + 1) - 3 = 48 x + 8 - 3 = 48 + 5 (g 鈭� f) (x) = 48 x + 5$

Part (c) Step 1. Given information

$f (x) = 6 x + 1 g (x) = 8 x - 3$

Part (c) Step 2. Calculation

$T o e v a l u a t e (f 路 g) (x), (f 路 g) (x) = f (x) . g (x) = (6 x + 1) 路 (8 x - 3) = 48 x^{2} - 18 x + 8 x - 3 = 48 x^{2} - 10 x - 3$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

For the functions, f(x) = 6x + 1 and
g(x) = 8x 鈭� 3, find:
$(a) (f 鈭� g) (x) (b) (g 鈭� f) (x) (c) (f 路 g) (x)$

Short Answer

Step by step solution

Part (a) Step 1. Given information

Part (a) Step 2. Calculation

Part (b) Step 2. Given information

Part (b) Step 2. Calculation

Part (c) Step 1. Given information

Part (c) Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Applied Mathematics

Statistics

Decision Maths

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

91影视

For the functions, f(x) = 6x + 1 andg(x) = 8x 鈭� 3, find:(a)(f鈭�g)(x)(b)(g鈭�f)(x)(c)(f路g)(x)

Short Answer

Step by step solution

Part (a) Step 1. Given information

Part (a) Step 2. Calculation

Part (b) Step 2. Given information

Part (b) Step 2. Calculation

Part (c) Step 1. Given information

Part (c) Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Applied Mathematics

Statistics

Decision Maths

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

For the functions, f(x) = 6x + 1 and
g(x) = 8x 鈭� 3, find:
$(a) (f 鈭� g) (x) (b) (g 鈭� f) (x) (c) (f 路 g) (x)$