Chapter 5: Q. 4 (page 348)

In Problems 2 – 4, for the given functions f and g find:
(a) (f o g)(2)
(b) (g o f) (-2)
(c) (f o f)(4)
(d) ( g o g) (-1)
$f (x) = e^{x} g (x) = 3 x - 2$

Short Answer

Expert verified

$(a) (f o g) (2) = e^{4} (b) (g o f) (- 2) = 3 e^{- 2} - 2 (c) (f o f) (4) = e^{e^{4}} (d) (g o g) (- 1) = - 17$

Step by step solution

Part(a) Step 1: Given Information

We are given with two functions

$f (x) = e^{x} g (x) = 3 x - 2$

Part(a) : Step 2: Composition of functions

$f (x) = e^{x} g (x) = 3 x - 2 (f o g) (2) = f (g (2)) g (2) = 3 (2) - 2 = 4 f (4) = e^{4} (f o g) (2) = e^{4}$

Part(b) : Step 1: composition of functions

$f (x) = e^{x} g (x) = 3 x - 2 (g o f) (- 2) = g (f (- 2)) f (- 2) = e^{- 2} g (e^{- 2}) = 3 e^{- 2} - 2 (g o f) (- 2) = 3 e^{- 2} - 2$

Part(c): Step 1: composition of functions

$f (x) = e^{x} g (x) = 3 x - 2 (f o f) (4) = f (f (4)) f (4) = e^{4} f (e^{4}) = e^{e^{4}} (f o f) (4) = e^{e^{4}}$

Part (d) : Step 1: composition of funcitons

$f (x) = e^{x} g (x) = 3 x - 2 (g o g) (- 1) = g (g (- 1) g (- 1) = 3 (- 1) - 2 = - 5 g (- 5) = 3 (- 5) - 2 = - 17 (g o g) (- 1) = - 17$

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.

In Problems 2 – 4, for the given functions f and g find:
(a) (f o g)(2)
(b) (g o f) (-2)
(c) (f o f)(4)
(d) ( g o g) (-1)
$f (x) = e^{x} g (x) = 3 x - 2$

Short Answer

Step by step solution

Part(a) Step 1: Given Information

Part(a) : Step 2: Composition of functions

Part(b) : Step 1: composition of functions

Part(c): Step 1: composition of functions

Part (d) : Step 1: composition of funcitons

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Mechanics Maths

Statistics

Logic and Functions

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 2 – 4, for the given functions f and g find:(a) (f o g)(2)(b) (g o f) (-2)(c) (f o f)(4)(d) ( g o g) (-1)f(x)=exg(x)=3x-2

Short Answer

Step by step solution

Part(a) Step 1: Given Information

Part(a) : Step 2: Composition of functions

Part(b) : Step 1: composition of functions

Part(c): Step 1: composition of functions

Part (d) : Step 1: composition of funcitons

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Mechanics Maths

Statistics

Logic and Functions

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 2 – 4, for the given functions f and g find:
(a) (f o g)(2)
(b) (g o f) (-2)
(c) (f o f)(4)
(d) ( g o g) (-1)
$f (x) = e^{x} g (x) = 3 x - 2$