Q. 5.21 For functionsf(x)=2x2鈭�4x+3聽an... [FREE SOLUTION]

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Intermediate Algebra

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$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q. 5.21 (page 496)

For functions $f (x) = 2 x^{2} 鈭� 4 x + 3$ and $g (x) = x^{2} 鈭� 2 x 鈭� 6$ 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

$\begin{array}{l} (a) (f + g) (x) = 3 x^{2} 鈭� 6 x 鈭� 3 \\ (b) (f + g) (3) = 6 \\ (c) (f 鈭� g) (x) = x^{2} 鈭� 2 x + 9 \\ (d) (f 鈭� g) (鈭� 2) = 17 \end{array}$

Step by step solution

Step 1. Given information

$\begin{array}{l} Thegivenfunctionsare \\ f (x) = 2 x^{2} 鈭� 4 x + 3 \\ g (x) = x^{2} 鈭� 2 x 鈭� 6 \end{array}$

We have to find

$\begin{array}{l} (a) (f + g) (x) \\ (b) (f + g) (3) \\ (c) (f 鈭� g) (x) \\ (d) (f 鈭� g) (鈭� 2) \end{array}$

Step 2. Solve for part (a)

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

Step 3. Solve for part (b)

$\begin{array}{l} Wehave (f + g) (x) = 3 x^{2} 鈭� 6 x 鈭� 3 \\ 鈬� (f + g) (3) = 3 {(3)}^{2} 鈭� 6 (3) 鈭� 3 [Substitute x = 3] \\ = 3 (9) 鈭� 18 鈭� 3 \\ = 27 鈭� 18 鈭� 3 \\ = 6 \end{array}$

Step 4. Solve for part (c)

$\begin{array}{l} Weknow (f 鈭� g) (x) = f (x) 鈭� g (x) \\ Substitutethefunctions f (x) and g (x) \\ 鈬� (f 鈭� g) (x) = (2 x^{2} 鈭� 4 x + 3) 鈭� (x^{2} 鈭� 2 x 鈭� 6) \\ = 2 x^{2} 鈭� 4 x + 3 鈭� x^{2} + 2 x + 6 [Rewritewithoutparentheses] \\ = 2 x^{2} 鈭� x^{2} 鈭� 4 x + 2 x + 3 + 6 [Putliketermstogether] \\ = x^{2} 鈭� 2 x + 9 \end{array}$

Step 5. Solve for part (d)

$\begin{array}{l} Wehave (f 鈭� g) (x) = x^{2} 鈭� 2 x + 9 \\ 鈬� (f 鈭� g) (鈭� 2) = {(鈭� 2)}^{2} 鈭� 2 (鈭� 2) + 9 [Substitute x = 鈭� 2] \\ = 4 + 4 + 9 \\ = 17 \end{array}$

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91影视

For functions $f (x) = 2 x^{2} 鈭� 4 x + 3$ and $g (x) = x^{2} 鈭� 2 x 鈭� 6$ 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 5. Solve for part (d)

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91影视

For functionsf(x)=2x2鈭�4x+3and g(x)=x2鈭�2x鈭�6 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 5. Solve for part (d)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Discrete Mathematics

Decision Maths

Statistics

Geometry

Calculus

Study anywhere. Anytime. Across all devices.

For functions $f (x) = 2 x^{2} 鈭� 4 x + 3$ and $g (x) = x^{2} 鈭� 2 x 鈭� 6$ find: $(a) (f + g) (x) (b) (f + g) (3) (c) (f 鈭� g) (x) (d) (f 鈭� g) (鈭� 2)$