Solve the following equation for x.

What is the domain of f/g given f(x) = x+4 and g(x) = x-1

Butoxors [25]

Answer: the domain of f/g is every real number except 1 which can be conventionally expressed as {(x,y): <em>x</em> ∈ R, x ≠ 1} OR (-∞ ≤ x < 1) ∩ (1< x ≤ ∞) OR x ∈ R; x ≠ 1.

Step-by-step explanation:

since f(x) = x + 4 and g(x) = x - 1

then f/g = x + 4/x - 1

the denominator of a function cannot be zero since a fraction with a denominator of zero is undefined.

∴ x - 1 ≠ 0

the value of x when g(x) = 0 is

x - 1 = 0

x = 1

∴ x ≠ 1

Therefore the domain of f/g is every real number except 1 which can be conventionally expressed as {(x,y): <em>x</em> ∈ R, x ≠ 1} OR (-∞ ≤ x < 1) ∩ (1< x ≤ ∞) OR x ∈ R; x ≠ 1.

5 0

3 years ago

Steve subscribed to 10 podcasts for a total of 340 minutes. He used his two favorite tags, Hobbies & Recreation and Soliloqu

Gwar [14]

We let x and y be the number of Hobbies & Recreation and Soliloquies episodes that Steve subscribe. The system of linear equation that best represent the given above is,
x + y = 10
32x + 42y = 340
The values of x and y from the system are 8 and 2, respectively. Thus Steve subscribed to 8 Hobbies & Recreation and to 2 Soliloquies episodes.

7 0

3 years ago

Duane and mick are saving their money to build a tree house.Duane adds $5 to their piggy bank every other week.Mick adds $2 ever

miss Akunina [59]

2 + 7 + 2 + 7 + 2 + 7 + 2 + 7 + 2 + 7 = 45
7 = 5 + 2
10 weeks

they have been saving their money for 10 weeks

6 0

3 years ago

Read 2 more answers

Which situation could be represented by the graph?

Ymorist [56]

The correct option which resembles with the given graph is $\fbox{\begin\\\ optionA and optionC\\\end{minispace}}$ .

Further explanation:

From the given graph the it is observed that the interval is $[8,11)$ which is a half open interval or it can be said that it is a half closed interval.

A half closed or a half open interval is an interval in which one end point of the interval is included but the other point is not included.

For example:

In an interval of the form $[a,b)$ the point $a$ is included in the set but the point $b$ is not included in the set.

Similarly, in the interval $[8,11)$ the point $8$ is included in the set but the point $11$ is not included in the set.

In order to determine the correct option which resembles with given graph form interval for each option.

Option A:

As per the statement in option A the age of the student must be at least $8$ years and not more than $11$ years that is the age of the student is either $8$ years or greater than $8$ years and less than $11$ years.

As per the above statement the interval formed is $\fbox{\begin\\\ [8,11)\\\end{minispace}}$ in which $8$ is included in the set and $11$ is not included which means it is a half closed or half opoen interval.

Therefore, $\fbox{\begin\\\ optionA\\\end{minispace}}$ is a correct option.

Option B:

As per the statement in option B the amount of money the babysitter can earn is between $\$8$ and $\$11$ per hour.

As per the above statement the interval formed is $\fbox{\begin\\\ (8,11)\\\end{minispace}}$ in which both of the end points are not included in the set which means that it is an open interval.

Therefore, $\fbox{\begin\\\ optionB\\\end{minispace}}$ is an incorrect option.

Option C:

As per the statement in option C the time required to complete a program in college cannot be less than $8$ hours and the time must be less than $11$ hours.

From the above statement it is concluded that the time required can be $8$ hours or more than $8$ hours but it has to be less than $11$ hours.

So, as per the above the statement the interval formed is $\fbox{\begin\\\ [8,11)\\\end{minispace}}$ .

Therefore, $\fbox{\begin\\\ optionC\\\end{minispace}}$ is a correct option.

Option D:

As per the statement in option D the age of the dogs is either $8$ years old or below $8$ years and age of the dog must be greater than $11$ tears.

As per the above statement the interval formed is $\fbox{\begin\\\ (-\infty,8) \bigcup(11,\infty)\\\end{minispace}}$ .

Therefore, the $\fbox{\begin\\\ optionD\\\end{minispace}}$ is an incorrect option.

So, $\fbox{\begin\\\ optionA and optionC\\\end{minispace}}$ are the correct options which resembles with the given graph.

Learn more:

A problem on composite function brainly.com/question/2723982
A problem to find radius and center of circle brainly.com/question/9510228
A problem to determine intercepts of a line brainly.com/question/1332667

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Sets

Keywords: Interval, set, open interval, closed interval, half open interval, half closed interval, set theory, program, community college, babysitters, veterinary clinic, ages, students.

5 0

3 years ago

Read 2 more answers

A line with a slope of -4 passes through the point

Viktor [21]

Answer:

y = -4x - 22

Step-by-step explanation:

m = -4

using (-6,2)

Slope-intercept: y = mx + b

2 = -4(-6) + b

2 = 24 + b

b = -22

y = -4x - 22

4 0

2 years ago