# The functions which have 5 in their domain. ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2.1, Problem 3E

(a)

To determine

## The functions which have 5 in their domain.

Expert Solution

The functions which have 5 in their domain are f(x)=x23x and g(x)=x5x .

### Explanation of Solution

Given:

The given functions are,

f(x)=x23x (1)

g(x)=x5x   (2)

h(x)=x10 (3)

Calculation:

The set of possible inputs for a function f is called the Domain of f.

For any real number the function f(x)=x23x gives a real value.

Therefore, the set of all real number is the domain of f(x)=x23x .

Since 5 is a real number, therefore 5 is the domain of f(x)=x23x .

For any real number except zero the function g(x)=x5x gives a real value.

Therefore, the set of all real number except zero {0} is the domain of g(x)=x5x .

Since 5 is a real number except zero, therefore 5 is the domain of g(x)=x5x .

For any real number greater than and equal to 10 the function h(x)=x10 gives a real value.

Therefore, the set of all real number greater than and equal to 10 is the domain of h(x)=x10 .

Since 5 is not a real number greater than and equal to 10, therefore 5 is not the domain of h(x)=x10 .

Thus, the functions which have 5 in their domain are f(x)=x23x and g(x)=x5x .

(b)

To determine

### The values of functions at x=5 who have 5 in their domain.

Expert Solution

The values of f(x)=x23x at x=5 is 10 and the value of g(x)=x5x at x=5 is 0.

### Explanation of Solution

Given:

From part (a), the functions which have 5 in their domain are given below,

f(x)=x23x

g(x)=x5x

Calculation:

Substitute 5 for x in equation (1), to find the value of f(x)=x23x at x=5 ,

f(5)=(5)23(5)=2515=10

For x=5 the function f(x)=x23x has a value 10.

Substitute 5 for x in equation (2) to find the value of g(x)=x5x at x=5 ,

g(5)=(5)5(5)=05=0

For x=5 the function g(x)=x5x has a real value 0.

Thus, the values of f(x)=x23x at x=5 is 10 and the value of g(x)=x5x at x=5 is 0.

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