Chapter 2: Q. 13 (page 124)

Find $f + g, f - g, f \cdot g$ and $\frac{f}{g}$ for each pair of functions. State the domain of each of these functions.
$f (x) = 3 x^{2} + x + 1 g (x) = 3 x$

Short Answer

Expert verified

For $f (x) = 3 x^{2} + x + 1; g (x) = 3 x$ , we get:

$f + g = 3 x^{2} + 4 x + 1$ and its domain is the set of all real numbers.

$f - g = 3 x^{2} - 2 x + 1$ and its domain is the set of all real numbers.

$f \cdot g = 9 x^{3} + 3 x^{2} + 3 x$ and its domain is the set of all real numbers.

$\frac{f}{g} = \frac{3 x^{2} + x + 1}{3 x}$ and its domain is ${x | x \neq 0}$ .

Step by step solution

Step 1. Given information

We have been given:

$f (x) = 3 x^{2} + x + 1 g (x) = 3 x$

We have to find $f + g, f - g, f \cdot g$ and $\frac{f}{g}$ for the pair of functions and state the domain of each of these functions.

Step 2. Find f+g and its domain.

We know $f + g = f (x) + g (x)$ .

Therefore,

$f + g = 3 x^{2} + x + 1 + 3 x = 3 x^{2} + 4 x + 1$

Its domain is the set of all real numbers.

Step 3. Find f-g and its domain.

We know $f - g = f (x) - g (x)$ .

Therefore,

$f - g = (3 x^{2} + x + 1) - (3 x) = 3 x^{2} + x + 1 - 3 x = 3 x^{2} - 2 x + 1$

Its domain is the set of all real numbers.

Step 4. Find f⋅g and its domain.

We know $f \cdot g = f (x) \cdot g (x)$ .

Therefore,

$f \cdot g = (3 x^{2} + x + 1) (3 x) = 9 x^{3} + 3 x^{2} + 3 x$

Its domain is the set of all real numbers.

Step 5. Find fg and its domain.

We know $\frac{f}{g} = \frac{f (x)}{g (x)}$ .

Therefore,

role="math" localid="1645974118795" $\frac{f}{g} = \frac{3 x^{2} + x + 1}{3 x}$

The domain will be the set of all real numbers except those that make the denominator zero.

$3 x = 0 x = 0$

The domain will be ${x | x \neq 0}$ .

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Find $f + g, f - g, f \cdot g$ and $\frac{f}{g}$ for each pair of functions. State the domain of each of these functions.
$f (x) = 3 x^{2} + x + 1 g (x) = 3 x$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find f+g and its domain.

Step 3. Find f-g and its domain.

Step 4. Find f⋅g and its domain.

Step 5. Find fg and its domain.

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Find f+g,f-g,f⋅gand fgfor each pair of functions. State the domain of each of these functions.f(x)=3x2+x+1g(x)=3x

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find f+g and its domain.

Step 3. Find f-g and its domain.

Step 4. Find f⋅g and its domain.

Step 5. Find fg and its domain.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

Find $f + g, f - g, f \cdot g$ and $\frac{f}{g}$ for each pair of functions. State the domain of each of these functions.
$f (x) = 3 x^{2} + x + 1 g (x) = 3 x$