Chapter 5: Q 514 (page 564)

For $f (x) = 2 x^{2} - 3 x - 5$ and $g (x) = 3 x^{2} - 4 x + 1$ find
(a) $(f + g) (x)$ $(f + g) (x)$
(b) $(f + g) (1)$ $(f + g) (1)$
(c) $(f - g) (x)$ $(f - g) (x)$
(d) $(f - g) (- 2)$

Short Answer

Expert verified

The required values are

(a) $(f + g) (x) = 5 x^{2} - 7 x - 4$

(b) $(f + g) (1) = - 6$

(c) $(f - g) (x) = \begin{array}{rcl} - \end{array} \begin{array}{rcl} x \end{array} \begin{array}{rcl} \end{array}$ ²+x-6

(d) $(f - g) (- 2) = - 12$

Step by step solution

Step 1. Given Information

The given polynomials are $f (x) = 2 x^{2} - 3 x - 5$ and $g (x) = 3 x^{2} - 4 x + 1$ .

Part (a) Step 1. Add the polynomials

Add the given polynomials as follows:

$\begin{array}{rcl} (f + g) (x) & = & 2 x^{2} - 3 x - 5 + 3 x^{2} - 4 x + 1 \\ = & 5 x^{2} - 7 x - 4 \end{array}$

So, the resultant expression is $5 x^{2} - 7 x - 4$ .

Part (b) Step 1. Given Information

The given expressions are $f (x) = 2 x^{2} - 3 x - 5$ and $g (x) = 3 x^{2} - 4 x + 1$ .

Part (b) Step 2. Substitution

Substitute $x = 1$ into $(f + g) (x) = 5 x^{2} - 7 x - 4$ .

$\begin{array}{rcl} (f + g) (1) & = & 5 {(1)}^{2} - 7 (1) - 4 \\ = & 5 - 7 - 4 \\ = & - 6 \end{array}$

So, $(f + g) (1) = - 6$ .

Part (c) Step 1. Given Information

The given expressions are $f (x) = 2 x^{2} - 3 x - 5$ and $g (x) = 3 x^{2} - 4 x + 1$ .

Part (c) Step 2.Subtract the Polynomials

Subtract $g (x)$ from $f (x)$ as follows:

$\begin{array}{rcl} (f - g) (x) & = & 2 x^{2} - 3 x - 5 - (3 x^{2} - 4 x + 1) \\ = & 2 x^{2} - 3 x - 5 - 3 x^{2} + 4 x - 1 \\ = & - x^{2} + x - 6 \end{array}$

So, the resulting polynomial is $\begin{array}{rcl} - x^{2} + x - 6 \end{array}$ .

Part (d) Step 1. Given Information

The given polynomials are $f (x) = 2 x^{2} - 3 x - 5$ and $g (x) = 3 x^{2} - 4 x + 1$ .

Part (d) Step 2. Substitution

Substitute $x = - 2$ into $(f - g) (x) = \begin{array}{rcl} - \end{array} \begin{array}{rcl} x \end{array} \begin{array}{rcl} \end{array}$ ²+x-6.

$\begin{array}{rcl} (f - g) (- 2) & = & - (- 2)^{2} + (- 2) - 6 \\ = & - 4 - 2 - 6 \\ = & - 12 \end{array}$

So, $(f - g) (- 2) = - 12$ .

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For $f (x) = 2 x^{2} - 3 x - 5$ and $g (x) = 3 x^{2} - 4 x + 1$ find
(a) $(f + g) (x)$ $(f + g) (x)$
(b) $(f + g) (1)$ $(f + g) (1)$
(c) $(f - g) (x)$ $(f - g) (x)$
(d) $(f - g) (- 2)$

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Add the polynomials

Part (b) Step 1. Given Information

Part (b) Step 2. Substitution

Part (c) Step 1. Given Information

Part (c) Step 2.Subtract the Polynomials

Part (d) Step 1. Given Information

Part (d) Step 2. Substitution

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For fx=2x2-3x-5and gx=3x2-4x+1find(a) (f+g)(x)(f+g)(x)(b) (f+g)(1)(f+g)(1)(c) (f-g)(x)(f-g)(x)(d)(f-g)(-2)

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Add the polynomials

Part (b) Step 1. Given Information

Part (b) Step 2. Substitution

Part (c) Step 1. Given Information

Part (c) Step 2.Subtract the Polynomials

Part (d) Step 1. Given Information

Part (d) Step 2. Substitution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Theoretical and Mathematical Physics

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Discrete Mathematics

Study anywhere. Anytime. Across all devices.

For $f (x) = 2 x^{2} - 3 x - 5$ and $g (x) = 3 x^{2} - 4 x + 1$ find
(a) $(f + g) (x)$ $(f + g) (x)$
(b) $(f + g) (1)$ $(f + g) (1)$
(c) $(f - g) (x)$ $(f - g) (x)$
(d) $(f - g) (- 2)$