Chapter 10: Q. 9 (page 1002)

In the following exercises, find the values described.
For functions , $f (x) = 2 x^{2} + 3$ and
$g (x) = 5 x - 1$ find
a. $f \circ g (- 2)$ ,
b. $g \circ f (- 3)$
c. $f \circ f (- 1)$

Short Answer

Expert verified

The value is $305, 104, 53$ respectively

Step by step solution

Given information

Given the function

$f (x) = 2 x^{2} + 3 g (x) = 5 x - 1$

Use composition and calculate

Using composition, we get

$f \circ g (x) = f [g (x)] f \circ g (x) = f (5 x - 1) f \circ g (x) = 2 {(5 x - 1)}^{2} + 3 f \circ g (x) = 2 (25 x^{2} - 10 x + 1) + 3 f \circ g (x) = 50 x^{2} - 20 x + 2 + 3 f \circ g (x) = 50 x^{2} - 20 x + 5 f \circ g (- 2) = 50 {(- 2)}^{2} - 20 (- 2) + 5 f \circ g (- 2) = 200 + 100 + 5 f \circ g (- 2) = 305$

Use the composition and calculate

Using composition, we get

$g \circ f (x) = g [f (x)] g \circ f (x) = g (2 x^{2} + 3) g \circ f (x) = 5 (2 x^{2} + 3) - 1 g \circ f (x) = 10 x^{2} + 15 - 1 g \circ f (x) = 10 x^{2} + 14 g \circ f (- 3) = 10 {(- 3)}^{2} + 14 g \circ f (- 3) = 104$

Use composition and calculate

Using composition, we get

$f \circ f (x) = f [f (x)] f \circ f (x) = f (2 x^{2} + 3) f \circ f (x) = 2 {(2 x^{2} + 3)}^{2} + 3 f \circ f (x) = 2 (4 x^{4} + 12 x^{2} + 9) + 3 f \circ f (x) = 8 x^{4} + 24 x^{2} + 18 + 3 f \circ f (x) = 8 x^{4} + 24 x^{2} + 21 f \circ f (- 1) = 8 {(- 1)}^{4} + 24 {(- 1)}^{2} + 21 f \circ f (- 1) = 8 + 24 + 21 f \circ f (- 1) = 53$

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 the following exercises, find the values described.
For functions , $f (x) = 2 x^{2} + 3$ and
$g (x) = 5 x - 1$ find
a. $f \circ g (- 2)$ ,
b. $g \circ f (- 3)$
c. $f \circ f (- 1)$

Short Answer

Step by step solution

Given information

Use composition and calculate

Use the composition and calculate

Use composition and calculate

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Theoretical and Mathematical Physics

Applied Mathematics

Pure Maths

Geometry

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, find the values described.For functions ,f(x)=2x2+3andg(x)=5x-1finda.f∘g(-2),b.g∘f(-3)c.f∘f(-1)

Short Answer

Step by step solution

Given information

Use composition and calculate

Use the composition and calculate

Use composition and calculate

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Theoretical and Mathematical Physics

Applied Mathematics

Pure Maths

Geometry

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, find the values described.
For functions , $f (x) = 2 x^{2} + 3$ and
$g (x) = 5 x - 1$ find
a. $f \circ g (- 2)$ ,
b. $g \circ f (- 3)$
c. $f \circ f (- 1)$