Q. 9 In the following exercises, find... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

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. $f 鈭� g (- 2)$ ,
b. $g 鈭� f (- 3)$
c. $f 鈭� f (- 1)$

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

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

Use the composition and calculate

Using composition, we get

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

Use composition and calculate

Using composition, we get

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

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91影视

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

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.

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91影视

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

Pure Maths

Statistics

Decision Maths

Discrete Mathematics

Mechanics Maths

Geometry

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. $f 鈭� g (- 2)$ ,
b. $g 鈭� f (- 3)$
c. $f 鈭� f (- 1)$