Intermediate Algebra

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$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q. 5.22 (page 496)

$Forfunctions f (x) = 5 x^{2} 鈭� 4 x 鈭� 1 and g (x) = x^{2} + 3 x + 8, find (a) (f + g) (x) (b) (f + g) (3) (c) (f 鈭� g) (x) (d) (f 鈭� g) (鈭� 2) .$

Short Answer

Expert verified

The value is

$\begin{array}{l} (a) (f + g) (x) = 6 x^{2} 鈭� x + 7 \\ (b) (f + g) (3) = 58 \\ (c) (f 鈭� g) (x) = 4 x^{2} 鈭� 7 x 鈭� 9 \\ (d) (f 鈭� g) (鈭� 2) = 21 \end{array}$

Step by step solution

Step 1. Given information

$\begin{array}{l} Thegivenfunctionsare \\ f (x) = 5 x^{2} 鈭� 4 x 鈭� 1 \\ g (x) = x^{2} + 3 x + 8 \\ (a) (f + g) (x) (b) (f + g) (3) (c) (f 鈭� g) (x) (d) (f 鈭� g) (鈭� 2) \end{array}$

Step 2. Solve for part (a)

$\begin{array}{l} Weknow (f + g) (x) = f (x) + g (x) \\ Substitutethefunctions f (x) and g (x) \\ 鈬� (f + g) (x) = (5 x^{2} 鈭� 4 x 鈭� 1) + (x^{2} + 3 x + 8) \\ = 5 x^{2} 鈭� 4 x 鈭� 1 + x^{2} + 3 x + 8 [Rewritewithoutparentheses] \\ = 5 x^{2} + x^{2} 鈭� 4 x + 3 x 鈭� 1 + 8 [Putliketermstogether] \\ = 6 x^{2} 鈭� x + 7 \end{array}$

Step 3. Solve for part (b)

$\begin{array}{l} Wehave (f + g) (x) = 6 x^{2} 鈭� x + 7 \\ 鈬� (f + g) (3) = 6 {(3)}^{2} 鈭� (3) + 7 [Substitute x = 3] \\ = 6 (9) 鈭� 3 + 7 \\ = 54 鈭� 3 + 7 \\ = 58 \end{array}$

Step 4. Solve for part (c)

$\begin{array}{l} Weknow (f 鈭� g) (x) = f (x) 鈭� g (x) \\ Substitutethefunctions f (x) and g (x) \\ 鈬� (f 鈭� g) (x) = (5 x^{2} 鈭� 4 x 鈭� 1) 鈭� (x^{2} + 3 x + 8) \\ = 5 x^{2} 鈭� 4 x 鈭� 1 鈭� x^{2} 鈭� 3 x 鈭� 8 [Rewritewithoutparentheses] \\ = 5 x^{2} 鈭� x^{2} 鈭� 4 x 鈭� 3 x 鈭� 1 鈭� 8 [Putliketermstogether] \\ = 4 x^{2} 鈭� 7 x 鈭� 9 \end{array}$

Step 4. Solve for part (d)

$\begin{array}{l} Wehave (f 鈭� g) (x) = 4 x^{2} 鈭� 7 x 鈭� 9 \\ 鈬� (f 鈭� g) (鈭� 2) = 4 x^{2} 鈭� 7 x 鈭� 9 [Substitute x = 2] \\ = 4 {(2)}^{2} 鈭� 7 (鈭� 2) 鈭� 9 \\ = 4 (4) + 14 鈭� 9 \\ = 16 + 14 鈭� 9 \\ = 21 \end{array}$

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91影视

$Forfunctions f (x) = 5 x^{2} 鈭� 4 x 鈭� 1 and g (x) = x^{2} + 3 x + 8, find (a) (f + g) (x) (b) (f + g) (3) (c) (f 鈭� g) (x) (d) (f 鈭� g) (鈭� 2) .$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve for part (a)

Step 3. Solve for part (b)

Step 4. Solve for part (c)

Step 4. Solve for part (d)

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91影视

Forfunctionsf(x)=5x2鈭�4x鈭�1andg(x)=x2+3x+8,find(a)(f+g)(x)(b)(f+g)(3)(c)(f鈭�g)(x)(d)(f鈭�g)(鈭�2).

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve for part (a)

Step 3. Solve for part (b)

Step 4. Solve for part (c)

Step 4. Solve for part (d)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Theoretical and Mathematical Physics

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Logic and Functions

Geometry

Study anywhere. Anytime. Across all devices.

$Forfunctions f (x) = 5 x^{2} 鈭� 4 x 鈭� 1 and g (x) = x^{2} + 3 x + 8, find (a) (f + g) (x) (b) (f + g) (3) (c) (f 鈭� g) (x) (d) (f 鈭� g) (鈭� 2) .$