Chapter 10: Q. 447 (page 1066)

For the functions, f(x) = 6x + 1 and
g(x) = 8x − 3, find:
$(a) (f \circ g) (x) (b) (g \circ f) (x) (c) (f \cdot g) (x)$

Short Answer

Expert verified

$(a) (f \circ g) (x) = 48 x - 17 (b) (g \circ f) (x) = 48 x + 5 (c) (f \cdot g) (x) = 48 x^{2} - 10 x - 3$

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

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

Part (b) Step 2. Given information

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

Part (b) Step 2. Calculation

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

Part (c) Step 1. Given information

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

Part (c) Step 2. Calculation

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

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

For the functions, f(x) = 6x + 1 and
g(x) = 8x − 3, find:
$(a) (f \circ g) (x) (b) (g \circ f) (x) (c) (f \cdot g) (x)$

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

Probability and Statistics

Geometry

Statistics

Decision Maths

Discrete Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

For the functions, f(x) = 6x + 1 andg(x) = 8x − 3, find:(a)(f∘g)(x)(b)(g∘f)(x)(c)(f·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

Probability and Statistics

Geometry

Statistics

Decision Maths

Discrete Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

For the functions, f(x) = 6x + 1 and
g(x) = 8x − 3, find:
$(a) (f \circ g) (x) (b) (g \circ f) (x) (c) (f \cdot g) (x)$