For each pair of function f and g below, find f(g(x)) and g(f(x)).

a. f(x)=3/x,x=/= 0
b. g(x)=3/x, x=/=0
c. f(x)=x+4
d. g(x)=-x+4

Answers

Answer 1

Answer:

(a) and (b)

[tex]f(g(x)) = g(f(x)) = x[/tex]

(c) and (d)

[tex]f(g(x)) =-x + 8[/tex]

[tex]g(f(x)) = x + 8[/tex]

Step-by-step explanation:

Given

(a) to (d)

Required

Find f(g(x)) and g(f(x)) for each pair

For (a) and (b), we have:

[tex]f(x) = \frac{3}{x}[/tex]

[tex]g(x) = \frac{3}{x}[/tex]

Calculate f(g(x))

[tex]f(x) = \frac{3}{x}[/tex]

[tex]f(g(x)) = \frac{3}{g(x)}[/tex]

Substitute 3/x for g(x)

[tex]f(g(x)) = \frac{3}{3/x}[/tex]

Rewrite as:

[tex]f(g(x)) = 3/\frac{3}{x}[/tex]

[tex]f(g(x)) = 3*\frac{x}{3}[/tex]

[tex]f(g(x)) = x[/tex]

Since f(x) = g(x), then:

[tex]f(g(x)) = g(f(x)) = x[/tex]

For (c) and (d)

[tex]f(x) =x + 4[/tex]

[tex]g(x) =-x + 4[/tex]

Solving f(g(x)), we have:

[tex]f(x) =x + 4[/tex]

[tex]f(g(x)) =g(x) + 4[/tex]

Substitute [tex]g(x) =-x + 4[/tex]

[tex]f(g(x)) =-x + 4 + 4[/tex]

[tex]f(g(x)) =-x + 8[/tex]

Calculating g(f(x))

[tex]g(x) =-x + 4[/tex]

[tex]g(f(x)) = -f(x) + 4[/tex]

Substitute: [tex]f(x) =x + 4[/tex]

[tex]g(f(x)) = x + 4 + 4[/tex]

[tex]g(f(x)) = x + 8[/tex]


Related Questions

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Which diagram shows the graph of y= -|x - 3|

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Answer:

y= -|x - 3| graph

Step-by-step explanation:

Choose the theorem that proves these triangles are congruent.

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SAS

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y = 2x+10 shows the price, y, for x hours of contractor labor. How much for 10 hours of labor?

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Answer:

$30

Step-by-step explanation:

Plus in 10 into the equation

Price=2(10)+10

Price=20+10

Price=30

Find the measure of Arc MP.

Answers

Answer:

use this formula

x/230×2×pie×radius

PN=180

MPN=MN=31

MP=x

180=31+x

x=180-31

x=149

Cos^2x+cos^2x*cot^2x

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Answer:

Cos^2x csc^2x

Step-by-step explanation:

Cos^2x (1 + cot^2x)

Please help me!!!!!!!!

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You have to multiply all the numbers to get the exact number and then you have to divide and multiply
U have to multiple all 3 than divide by 28 so I got 3085.71428571

im sooooooooo bord sooooo you get 100 points for ansering 1+1¥¥¥¥¥¥¥¥

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Answer:

1+1=2

Step-by-step explanation:

THANKS YOU YAY HOPE IT HEOPS

Answer:

2 thanks

Step-by-step explanation:

Reduce la siguiente expresión algebraica:
E(x,y)=x3y5+3y5x3+12x3y5−2y5x3
es para hoy

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Answer:

123456789101112131415161718192021222324252627

You wonder what is the average number of credits Le Moyne students take per semester. You speak with the Le Moyne registrar, and they tell you that Le Moyne students take an average of 17 credits per semester with a population standard deviation of 2.5 credits. We plan to take a sample of 49 students and ask each student how many credits they plan to take. Assume that the population mean is 17 credits and the populations standard deviation is 2.5 credits. What does the CLT say about the distribution of the sample mean of 49 students

Answers

Answer:

The CLT says that the distribution is approximately normal, with mean of 17 credits and standard deviation of 0.3571 credits.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Assume that the population mean is 17 credits and the populations standard deviation is 2.5 credits.

This means that [tex]\mu = 17, \sigma = 2.5[/tex]

What does the CLT say about the distribution of the sample mean of 49 students?

It is approximately normal.

The mean is 17.

Due to the sample of 49, n = 49, and the standard deviation is [tex]s = \frac{2.5}{\sqrt{49}} = 0.3571[/tex]

The CLT says that the distribution is approximately normal, with mean of 17 credits and standard deviation of 0.3571 credits.

Help me with my homework, please

Answers

Answer:

150°

Step-by-step explanation:

We know each angle in a equilateral triangle is 60° and that of a rectangle is 90° . So ,

[tex]\implies \angle ABC = \angle DBC + \angle ABD \\\\\implies \angle ABC = 90^o + 60^o \\\\\implies \boxed{\boxed{ \angle ABC = 150^o }}[/tex]

A village wishes to measure the quantity of water that is piped to a factory during a typical morning. A gauge on the water line gives the flow rate (in cubic meters per hour) at any instant. The flow rate is about 100 m3/hr at 6 am and increases steadily to about 280 m3/hr at 9 am. Using only this information, give your best estimate of the total volume of water used by the factory between 6 am and 9 am.

Answers

Answer:

570 m³

Step-by-step explanation:

The volume of water is the product of flow rate of water and the time taken. We are to get the volume of water used between 6 am and 9 am, that is for 3 hours (9 - 6).

We are given the flow rate at 6 am and the flow rate at 9 am, but this flow rate changes between 6 am and 9 am. To get the estimate of the water used, Let us assume that it flows at the same flow rate as it was at 6 am throughout, hence:

[tex]V_L= 100 m^3/h * 3h=300\ m^3[/tex]

Also, let us assume that it flows at the same flow rate as it was at 9 am throughout, hence:

[tex]V_R= 280 m^3/h * 3h=840\ m^3[/tex]

To get the best estimate of the total volume, let us find the average of the two values, hence:

[tex]Volume=\frac{V_L+V_R}{2} =\frac{300+840}{2}=570\ m^3[/tex]

A car wash attendant counted the number of cars washed and the total amount of money earned. The company charged the same price for each car washed and earned $165 for 15 cars, $231 for 21 cars, and $275 for 25 cars. Write an equation for the relationship between the number of cars washed, n, and the number of dollars earned, m.

Answers

The answer is m(n)= 11n
If you take the different of the money from 21 cars and 25 cars, you get 44 and since 21 and 25 is only a difference of 4, you’ll divide the 44 earned by the 4 cars washed to get $11 per car and then just make sure to use the correct variables

Abdul earns 44 dollars per week working part-time at a book store. He makes one dollar more for each book that he sells. The amount, A (in dollars), that Abdul
earns in a week if he sells b books is given by the following function.
A(b) = 44+b
How much does Abdul earn in a week if he sells 31 books?

Answers

Answer:

$75

Step-by-step explanation:

he makes $44 and then you add the dollar per 31 books making $75

Use the ALEKS calculator to find 35% of 67. Do not round your answer.

Answers

Answer:

23.45

Step-by-step explanation:

35 percent of 67=23.45

35×67=2345

2345/100=23.45

Ryan has constructed a multiple regression model and wants to test some assumptions of his regression model. In particular, he is testing for normality of the residuals. To do this Ryan should:
a. construct a normal quantile plot of the residuals and see if the result is an approximately upward sloping straight line
b. plot the residuals vs the predicted values of the response variable and check if the result is a random pattern
c. plot the residuals vs the observed values of the response variable and check if it forms and upward sloping line
d. plot the residuals vs each explanatory variable to check if they are approximately random and form no clear pattern
e. construct a normal quantile plot of the residuals and see if the result is an approximately horizontal straight line
f. construct a normal quantile plot of the residuals and see if the result is an approximately downward sloping straight line

Answers

Answer:

plot the residuals vs the observed values of the response variable and check if it forms and upward sloping line ( C )

Step-by-step explanation:

Ryan should plot the residuals vs the observed values of the response variable and check if it forms and upward sloping line ( C )

The exact right action on what Ryan should do is not listed in the options listed below, hence I have just picked the closest on what Ryan should do if he is testing for normality of the residuals after constructing a multiple regression model

Normality of residuals test is performed to ensure that the residuals are properly/evenly distributed

help me for a brianly

Answers

Answer:

35

Step-by-step explanation:

you multiply like it is a rectangle then you cut your answer in half in this case 7x10=70 cut in half is 35

2.6x + 10.5 = 31.3
I need to find the answer of x whoever gets it correct will get brianliest!

Answers

Answer:

2.6x + 10.5 = 31.3

Step-by-step explanation:

the correct answer is x=8


The population of rabbits in a forest follows the law of
exponential
growth.
If 90 rabbits are present initially and
there are 180 after 3 years, how many will here be in 4 yours

Answers

Answer:

226.78579

Step-by-step explanation

first, find k in 90(3^kx)

90(e^0) = 90 [when time is 0 years, the population is 90]

180=90(e^k3), 2=e^3k

ln2 = 3k, k=(ln2)/3

90(e^4(ln2)/3) = 90(e^ln(16)/3)

it is about 226.78579

Please help me with this I'm having some trouble

Answers

obtuse: B

straight: C

acute: A

right: D

Step-by-step explanation:

Draw a clock and put the hands on the clock and you can see the angel that the clock has.

During a school fund-raiser, the Student Government Association tracked the
average donation by student. Which of the following can you conclude about
the fund-raiser?
Average Number of Dollars Donated
to Kennedy High School, by Grade
120
100
80
60
Average donation (S)
20
0
9th
10th
12th
11th
Grade
A. The higher the grade, the larger the average donation.
O B. The school raised a total of $100.
c. 100 12th graders donated to the fund-raiser.
D. The school raised $271.

Answers

Answer:

A) The higher the grade, the larger the average donation

Answer:

The Answer is A

Step-by-step explanation:

PLZZZ HELP!!!!!!!!!1
What is the median and Q1 of the data set represented on the plot?

Median = 30; Q1 = 20
Median = 33; Q1 = 20
Median = 30; Q1 = 25
Median = 33; Q1 = 25

Answers

Answer:

i cant put the picture

Step-by-step explanation:

d. Median=33;Q1=25 the median is represented by the line in between the two boxes. Q1 is represented by the line on the far left of the box in the picture Q1 is marked for quadrent 1 and m is for median

The diagram shows Maha's garden.

AB = 15.3 m.
BC= 13.6m.
AD = 24.0m.
Find the perimeter of the garden.​

Answers

Answer:

perimeter = 71.4 m

Step-by-step explanation:

using the Pythagorean theorem:

CD² = 15.3² + (24 - 13.6)² = 234.09 + 108.16 = 342.25

CD = √342.25 = 18.5

perimeter = 24 + 15.3 + 13.6 + 18.5 = 71.4 m

Find cos 0
16
20
12
A.
12
16
B.
12
20
C.
16
20
10
D.

Answers

Answer:

b cuz its cosine but i flipped the numbers so it can be 20 over 12 and gave me exactly 0

The trigonometric function gives the ratio of different sides of a right-angle triangle. The value of cos(θ) in the given triangle is 0.6.    

What are Trigonometric functions?

The trigonometric function gives the ratio of different sides of a right-angle triangle.

[tex]\rm \sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\\cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\\tan \theta=\dfrac{Perpendicular}{Base}\\\\\\[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

In a right angle, the cosine function of trigonometry is the ratio of the base of the triangle and the hypotenuse of the triangle.

For angle θ, the dimension of the triangle will be,

Perpendicular = 16

Base = 12

Hypotenuse = 20

Now, the measure of cos(θ) will be,

Cos(θ) = Base / Hypotenuse

           = 12 / 20

           = 6 / 10

           = 0.6

Hence, the value of cos(θ) in the given triangle is 0.6.

Learn more about Trigonometric functions here:

https://brainly.com/question/6904750

#SPJ5

The experimental probability that Kevin will catch a
fly ball is equal to 3/4. About what percent of the
time will Kevin catch a fly ball?

A. 77%
B.55%
C.88%
D.75%

Answers

Answer:

C.

Step-by-step explanation:

Answer:

75%

Step-by-step explanation:

The fraction 3/4 is equivalent to 75%. Therefore, the percent Kevin will catch a fly ball is 75%.

Find the value of x. Round to the nearest tenth. x=
27 , 34 , 11 ,


Will give brainliest

Answers

Answer:

13.5

Step-by-step explanation:

your teacher wrote all the tools you need down already.

we only need to apply them.

is that really so difficult ?

because of the law of sines we have

sin(27)/11 = sin(34)/x

we can also turn this upside down to simplify the calculation.

11/sin(27) = x/sin(34)

x = 11×sin(34)/sin(27) = 13.549 ≈ 13.5

there, that was all there was to it ...

(NO LINKS)

Please help this assignment is over due and I don't get it

Answers

Answer:

B + 8 = 17 (just incase you need it, B = 9)

Step-by-step explanation:

Hope this helps, pls try to turn it in soon! :))

B is 9 because 8 + 9 is equal to 17

The height meters of a mass projected vertically upwards at a time seconds s=ut-0.5gt².
Determine how long the mass will take after being projected to reach a height of 16m on the ascent.
b. on the descent when u=30m/s and g=9.8m/s​

Answers

9514 1404 393

Answer:

  t ≈ 0.590 s (ascent); 5.532 s (descent)

Step-by-step explanation:

We are interested in the values of t when s=16.

  s = 30t -4.9t²

  4.9t^2 -30t +16 = 0 . . . . . substitute 16 for s; put in standard form

The quadratic formula can be used to find the solutions:

  t = (-(-30) ±√((-30)² -4(4.9)(16)))/(2(4.9))

  t = (30 ±√586.4)/9.8 ≈ 0.59023, 5.53221 . . . . seconds after launch

a) It will take 0.590 seconds to reach 16 m height initially.

b) It will take 5.532 seconds to return to 16 m height on descent.

Solve the simultaneous equations
2x - 5y = 9
3x + 4y = 2

Answers

Answer:

x = 2

y = 1

Step-by-step explanation:

Answer:

x= 2

y= -1

Step-by-step explanation:

Find the area of the semicircle. Enter the an exact answer in terms of or use 3.14 for and enter your answer as a decimal. PLEASE ANSWER NOW!

Answers

Answer:

6.28 units²

Step-by-step explanation:

The formula for finding the area of a circle:

πr²

We are given r = 2. So,

π(2)²

12.56 units²

However, it is a semicircle. So, only half of this value is needed.

12.56/2 = 6.28 units²

Answer:

area =12.56

Step-by-step explanation:

area of a semicircle=(pi(r)^2)/2

(3.14(2)^2)/2

(3.14(4))/2

12.56/2

6.28

A manufacturing company produces 275 units per day currently. The company's goal is to increase the number of units
manufactured per day by 50 each year. If the company meets its goal, how many units will it be producing per day 8 years
from now?
Select the correct answer below:
333
400
625
675
725

Answers

Answer:

D) 675 units per day.

Step-by-step explanation:

We can write a function to model the situation.

The company is currently producing 275 units per day.

And it will increase its production by 50 units after each year.

Therefore, after y years, its production in units per day will be:

[tex]f(y)=275+50y[/tex]

Then 8 years from now, the company will be producing:

[tex]f(8)=275+50(8)=275+400=675\text{ units per day.}[/tex]

Our answer is D.

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