Chapter 5: Q. 5.21 (page 496)

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

Short Answer

Expert verified

The value is

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

Step by step solution

Step 1. Given information

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

We have to find

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

Step 2. Solve for part (a)

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

Step 3. Solve for part (b)

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

Step 4. Solve for part (c)

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

Step 5. Solve for part (d)

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

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

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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For functionsf(x)=2x2−4x+3and g(x)=x2−2x−6 find:(a)(f+g)(x)(b)(f+g)(3)(c)(f−g)(x)(d)(f−g)(−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

Discrete Mathematics

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Calculus

Study anywhere. Anytime. Across all devices.

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