Intermediate Algebra (13th Edition)
Intermediate Algebra (13th Edition)
13th Edition
ISBN: 9780134707365
Author: Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson
Publisher: PEARSON
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Textbook Question
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Chapter D, Problem 1DE

Given f ( x ) = x 2 + 3 and g ( x ) = x 2 3 find each of the following.

a. ( f + g ) ( x )

b. ( f g ) ( x )

c. ( f g ) ( x )

d. ( f / g ) ( x )

e. ( f f ) ( x )

(a)

Expert Solution
Check Mark
To determine

To calculate: The expression which represents (f+g)x for the functions, f(x)=x2+3,g(x)=x23.

Answer to Problem 1DE

Solution:

The required expression for the provided functions f(x)=x2+3,g(x)=x23 is (f+g)x=2x2.

Explanation of Solution

Given information:

Two functions,

f(x)=x2+3g(x)=x23

Formula used:

Addition of two functions,

If there are two functions f(x),g(x).

Then,

(f+g)x=f(x)+g(x)

Calculation:

Consider the functions provided.

f(x)=x2+3g(x)=x23

Use the principal of addition of two functions if the functions are f(x),g(x).

(f+g)x=f(x)+g(x)

Therefore,

(f+g)x=f(x)+g(x)=(x2+3)+(x23)(f+g)x=2x2

Hence, the addition of the functions is (f+g)x=2x2.

(b)

Expert Solution
Check Mark
To determine

To calculate: The expression which represents (fg)x for the functions, f(x)=x2+3,g(x)=x23.

Answer to Problem 1DE

Solution:

The required expression for the provided functions f(x)=x2+3,g(x)=x23 is (fg)x=6.

Explanation of Solution

Given information:

Two functions,

f(x)=x2+3g(x)=x23

Formula used:

Subtraction of two functions,

If there are two functions f(x),g(x).

Then,

(fg)x=f(x)g(x)

Calculation:

Consider the functions provided.

f(x)=x2+3g(x)=x23

Use the principal of subtraction of two functions if the functions are f(x),g(x).

(fg)x=f(x)g(x)

Therefore,

(fg)x=f(x)g(x)=(x2+3)(x23)=x2+3x2+3(fg)x=6

Hence, the required expression for the provided functions f(x)=x2+3,g(x)=x23 is (fg)x=6.

(c)

Expert Solution
Check Mark
To determine

To calculate: The expression which represents (fg)x for the functions, f(x)=x2+3,g(x)=x23.

Answer to Problem 1DE

Solution:

The required expression for the provided functions f(x)=x2+3,g(x)=x23 is (fg)x=x49.

Explanation of Solution

Given information:

Two functions,

f(x)=x2+3g(x)=x23

Formula used:

Multiplication of two functions.,

If there are two functions f(x),g(x).

Then,

(fg)x=f(x)g(x)

Calculation:

Consider the functions provided.

f(x)=x2+3g(x)=x23

Use the principal of multiplication of two functions if the functions are f(x),g(x).

(fg)x=f(x)g(x)

Therefore,

(fg)x=f(x)g(x)=(x2+3)(x23)(fg)x=x49

Hence, the required expression for the provided functions f(x)=x2+3,g(x)=x23 is (fg)x=x49.

(d)

Expert Solution
Check Mark
To determine

To calculate: The expression which represents (fg)x for the functions, f(x)=x2+3,g(x)=x23.

Answer to Problem 1DE

Solution:

The required expression for the provided functions f(x)=x2+3,g(x)=x23 is (fg)x=x2+3x23.

Explanation of Solution

Given information:

Two functions,

f(x)=x2+3g(x)=x23

Formula used:

Division of two functions.,

If there are two functions f(x),g(x).

Then,

(fg)x=f(x)g(x)

Calculation:

Consider the functions provided,

f(x)=x2+3g(x)=x23

Use the principal of division of two functions if the functions are f(x),g(x).

(fg)x=f(x)g(x)

Therefore,

(fg)x=f(x)g(x)(fg)x=x2+3x23

Hence, the required expression for the provided functions f(x)=x2+3,g(x)=x23 is (fg)x=x2+3x23.

(e)

Expert Solution
Check Mark
To determine

To calculate: The expression which represents (ff)(x) for the function, f(x)=x2+3.

Answer to Problem 1DE

Solution:

The required expression for the provided function f(x)=x2+3. (ff)(x)=(x2+3)2.

Explanation of Solution

Given information:

A function,

f(x)=x2+3

Formula used:

Multiplication of a function with itself.

If there a function,

Then,

(ff)(x)=f(x)f(x)

Calculation:

Consider the function provided.

f(x)=x2+3

Use the principal of multiplication of function with itself.

(ff)(x)=f(x)f(x)

Therefore,

(ff)(x)=f(x)f(x)=(x2+3)(x2+3)(ff)(x)=(x2+3)2

Hence, the expression that represents the required function is (ff)(x)=(x2+3)2.

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