Consider the following functions. f(x) = x2, g(x) = x + 9 Find (f ∘ g)(x). Find the domain of (f ∘ g)(x). (Enter your answer using interval notation.) Find (g ∘ f)(x). Find the domain of (g ∘ f)(x). (Enter your answer using interval notation.) Find (f ∘ f)(x). Find the domain of (f ∘ f)(x). (Enter your answer using interval notation.) Find (g ∘ g)(x). Find the domain of (g ∘ g)(x). (Enter your answer using interval notat

Answers

Answer 1

Answer:

Whe we have two functions, f(x) and g(x), the composite function:

(f°g)(x)

is just the first function evaluated in the second one, or:

f( g(x))

And the domain of a function is the set of inputs that we can use as the variable x, we usually start by thinking that the domain is the set of all real numbers, unless there is a given value of x that causes problems, like a zero in the denominator, for example:

f(x) = 1/(x + 1)

where for x = -1 we have a zero in the denominator, then the domain is the set of all real numbers except x = -1.

Now, we have:

f(x) = x^2

g(x) = x + 9

then:

(f ∘ g)(x) = (x + 9)^2

And there is no value of x that causes problems here, so the domain is the set of all real numbers, that, in interval notation, is written as:

x ∈ (-∞, ∞)

(g ∘ f)(x)

this is g(f(x)) = (x^2) + 9 = x^2 + 9

And again, here we do not have any problem with a given value of x, so the domain is again the set of all real numbers:

x ∈ (-∞, ∞)

(f ∘ f)(x) = f(f(x)) = (f(x))^2 = (x^2)^2 = x^4

And for the domain, again, there is no value of x that causes a given problem, then the domain is the same as in the previous cases:

x ∈ (-∞, ∞)

(g ∘ g)(x) = g( g(x) ) = (g(x) + 9) = (x + 9) +9 = x + 18

And again, there are no values of x that cause a problem here, so the domain is:

x ∈ (-∞, ∞)


Related Questions

Heyy!! Can someone help me please!!

3 (5x + 2) - 2 (4x -4)

I don’t know what to doooo!!

Answers

Answer:

7x + 14

Step-by-step explanation:

the first thing to do is expand the parentheses/brackets.

3(5x + 2) -2(4x - 4) will be

3(5x) + 3(2) -2(4x) -2(-4)

= 15x + 6 - 8x + 8

collect like terms

15x - 8x + 6 + 8 = 7x + 14

the answer is 7x + 14

Answer:

3(5x+2)-2(4x-4)

15x+6-8x+8

15x-8x+6+8

7x+14

The circle shown has a radius of 4 cm.
What is the area of the circle to 1 decimal place?

Answers

Answer:

A = 50.2 cm^2

Step-by-step explanation:

The area of a circle is given by

A = pi r^2  where r is the radius

A = (3.14) * 4^2

A =50.24

To 1 decimal place

A = 50.2 cm^2

Answer:

50.3 cm^2 to 1 dec. place.

Step-by-step explanation:

Area = pi r^2

= pi * 4^2

= 16 * pi

= 50.265

consider the polygon shown. Determine the value of y. PLEASE HELP​

Answers

Answer:

y = 64°

Step-by-step explanation:

From the picture attached,

m(∠E) = 90°

m(∠E) = m(∠D)

m(∠B) + 67° = 180° [pair of linear angles]

m(∠B) = 113°

m(∠C) + 75° = 180°

m(∠C) = 180° - 75°

           = 105°

Since, sum of interior angles of a polygon = (n - 2) × 180°

Here, n = number of sides

For n = 5,

Sum of interior angles = (5 - 2) × 180°

                                     = 540°

m(∠A) + m(∠B) + m(∠C) + m(∠D) + m(∠E) = 540°

m(∠A) + 113° + 105° + m(∠D) + 90° = 540°

(m∠D) + m(∠D) = 540 - 308 [Since, m(∠A) = m(∠D)]

2(m∠D) = 232

m(∠D) = 116°

m(∠D) + y° = 180° [Linear pair of angles]

116 + y = 180

y = 64°

Here is some record keeping from a coffee shop about their paper cups. Cups are delivered 2,000 at a time. day change Monday +2000 Tuesday -125 Wednesday -127 Thursday +1719 Friday -356 Saturday -782 Sunday 0 1. Explain what a positive and negative number means in this situation. PLEASE HELP ME​

Answers

Answer: the numbers with the plus sign are positive and the ones with the negative sign are negative

Step-by-step explanation:

Express the null hypothesis and the alternative hypothesis in symbolic form.

Use the correct symbol (μ,p,σ) for the indicated parameter.

A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz.

a. H0: μ<14
H1: μ≥14

b. H0: μ=14
H1: μ<14

c. H0: μ>14
H1: μ≤14

d. H0: μ=14
H1: μ>14

Answers

Answer:

a. H0: μ<14

H1: μ≥14

Step-by-step explanation:

Mean symbol:

The mean symbol is given by [tex]\mu[/tex]

A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz.

At the null hypothesis, we test if the proportion is of less than 14 oz, that is:

[tex]H_0: \mu < 14[/tex]

At the alternative hypothesis, we test if this proportion is of at least 14 oz, that is:

[tex]H_1: \mu \geq 14[/tex]

So the correct answer is given by option a.

The Boffo Product Company sells a waffle iron on which they have done product testing. They have determined that the amount of time the product will last can be described by a normal distribution. In particular, the average waffle iron lasts for 12 years and one standard deviation is 8 months. How long should they warranty the product for if they want no more than 6.7% of the waffle irons to fail within that time

Answers

Answer:

They should warranty the product for 7 years if they want no more than 6.7% of the waffle irons to fail within that time.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The average waffle iron lasts for 12 years and one standard deviation is 8 months.

Measuring the time in months, we have that [tex]\mu = 12*8 = 96[/tex] and [tex]\sigma = 8[/tex]

How long should they warranty the product for if they want no more than 6.7% of the waffle irons to fail within that time?

This is X when Z has a p-value of 0.067, so X when Z = -1.5. Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.5 = \frac{X - 96}{8}[/tex]

[tex]X - 96 = -1.5*8[/tex]

[tex]X = 84[/tex]

84 months = 7 years.

They should warranty the product for 7 years if they want no more than 6.7% of the waffle irons to fail within that time.

You perform an experiment in which you take 16 pots of strawberry plants and give half of them 1 gm of ammonium nitrate per liter of water and the other half receive only water. Each group is then split in half again, and exposed to either 8 or 16 hours of light each day. You monitor the height of the plants for 4 weeks. You observe that plants grown in ammonium nitrate and 16 hours of light grow taller than no ammonium nitrate and 8 hours of light. Which of the following are dependent variables in this experiment?
A. An independent variable.
B. A dependent variable.
C. A controlled variable.
D. Either an independent or dependent variable.
E. Either a dependent or standardized variable.

Answers

I feel like the answer is B

It is influenced by the independent variables, such as the presence or absence of ammonium nitrate and the duration of light exposure.

Therefore, the correct answer is B. A dependent variable.

Here, we have,

In this experiment, the dependent variable is the variable being measured or observed as the outcome.

It is what we are interested in studying and can be influenced by the independent variables.

In the given scenario, the height of the plants is being monitored over the four weeks.

This height measurement is the outcome of the experiment and is the dependent variable.

It is influenced by the independent variables, such as the presence or absence of ammonium nitrate and the duration of light exposure.

Therefore, the correct answer is B. A dependent variable.

To learn more on experiment click:

https://brainly.com/question/16979203

#SPJ4

Please help me please !

Answers

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

Option C

»»————- ★ ————-««  

Here’s why:

⸻⸻⸻⸻  

[tex]\text{\underline{The Slope Formula Is:}}\\\\m=\frac{y_2-y_1}{x_2-x_1}\\\\(x_1,y_1)\text{ and } (x_2,y_2)\text{ are two points given.}\\\\\text{We are given the points: } (3,5) \text{ and } (9,2).\\\\\text{\underline{The formula for the points should be:}}\\\\m=\frac{5-2}{3-9}, \text{where } (9,2) \text{ is }(x_1,y_1)\text{ and } (3,5) \text{ is } (x_2,y_2).[/tex]

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

need help asap plz!!!!!

Answers

Answer:

Step-by-step explanation:

In the simplest way, the domain of a function is basically all of the possible values of the input variable or x-axis in a graph. While the range of a function would be all of the real possible outputs that the function can create. In a graph this would be all of the possible values for the y-axis. For example, in the following function...

y = 4x + 3

The domain of this function would be any and all values for x, while the range of the function would be any and all values that the function can output for y.

Is there a local minimum at x= -4?

Answers

9514 1404 393

Answer:

  yes

Step-by-step explanation:

Yes, the turning point at (-4, -16) is a local minimum. It is a minimum because the curve goes upward either side of it. It is local (not global) because the curve has values that are lower than -16 at other values of x.

__

Similarly, the point (4, 16) is a local maximum.

Question 5 of 10 If f(x) = 3x-2 and g(x) = x2 +1, find (f +9)(x). A. x2 + 3x+1 B. x2 + 3x-1 C. 472–1 D. 2x+3​

Answers

Answer:

(3x+2)^2+1

Step-by-step explanation:

Find csc0

Please Help!!!!!

Answers

Answer:  -5/4

=======================================================

Explanation:

The terminal point is at (x,y) = (3,-4)

Apply the pythagorean theorem to find that x^2+y^2 = r^2 solves to r = 5. This is the length of the hypotenuse.

Then we can determine the cosecant of the angle theta using the formula below

csc(theta) = hypotenuse/opposite

csc(theta) = r/y

csc(theta) = 5/(-4)

csc(theta) = -5/4

Side note: csc = 1/sin

-5/4 maybe is the correct answer

How do you solve x[tex]x^{2} +4x+3=0[/tex]?

Answers

Answer:

[tex]{ \tt{ {x}^{2} + 4x + 3 = 0}} \\ { \tt{(x + 1)(x + 3) = 0}} \\ \\ { \tt{x = - 1 \: \: and \: \: - 3}}[/tex]

Write the word sentence as an equation.

The quotient of a number n and 5 is 18.

Answers

Answer:

n/5 = 18

Step-by-step explanation:

Quotient means division.

n/5 = 18

help me pleaseeeee it’s timedddddd

Answers

Answer:

10feet

Step-by-step explanation:

Given the following

Horizontal distance adjacent )= 15feet

Angle of elevation = 33.69°

Required

Height (opposite)

Using the SOH CAHTOA identity

tan theta = opposite/adjacent

tan 33.69 = H/15

H = 15tan33.69

H = 15(0.6667)

H = 9.999

H = 10feet to the nearesst foot

What is the value of c?
A. 68
B. 71
C. 38
D. 34

Answers

Answer: C

Step-by-step explanation:

See diagram above

Plot the image of point B under a reflection across line m

Answers

Answer:

Step-by-step explanation:

If a point (x, y) is reflected across a line, image of the point will be at the same distance from the line as the original point is.

In fact line of reflection works like a mirror.

In the figure attached,

Distance of point B from the line 'm' = 6 units

Therefore, distance of the image point B' from line 'm' = 6 units (on opposite side of the line of reflection)

For each of the following properties write down a matrix that has this property or explain why there is no such matrix (Hint: Check first whether the dimensions add up)
(a) The column space contains (1,0,0)T, (0,0,1)T while the row space contains (1,1)T and (1, 2)T.
(b) The column space is generated by (1,1,1)7T, the null space (or kernel) is generated by (1,2,3)T
(c) The column space is R4 and the row space is R3.

Answers

Answer:

a) A =   [tex]\left[\begin{array}{ccc}1&0\\0&0\\0&1\end{array}\right][/tex] 3*2

b) attached below ( Matrix dose not exist )

c) attached below  ( Matrix does not exist )

Step-by-step explanation:

a) Matrix

A =   [tex]\left[\begin{array}{ccc}1&0\\0&0\\0&1\end{array}\right][/tex] 3*2

From the matrix ; Column 1 and Column 2 Belong to COL(A)

while : (1,1)^T  =  ( 1,0 )^T +  ( 0,1 )^T  i.e. (1,1)^T  ∈  Row( A )

and (1, 2)^T. = ( 1,0 )^T + 2 ( 0,1 )^T   i.e. (1, 2)^T  ∈  Row( A )

Hence ; all requirements are fulfilled in Matrix A

b)  The column space is generated by (1,1,1)7T, the null space (or kernel) is generated by (1,2,3)T

Matrix is Non-existent because condition is not met

attached below

c) Rank | A |

dimension of column space= 4 , dimension of Row space = 3

Given that ; column space ≠ Row space

Hence Matrix does not exist

How does this post work?

Answers

B is the correct answer since we are finding the perimeter of a rectangle
54 1/8+54 1/8= 108 1/4
38 1/2+38 1/2= 77
108 1/4+77= 185.25

So B is the answer

A.54 pie cm^3

B.72 pie cm^3

C.126 pie cm^3

D.378 pie cm^3

Answers

Answer:  54pi  cm^3   (choice A)

==========================================================

Explanation:

The radius of each sphere is r = 3

The volume of one sphere is

V = (4/3)*pi*r^3

V = (4/3)*pi*3^3

V = 36pi

That's the volume of one sphere.

Three spheres take up 3*36pi = 108pi cm^3 of space.

---------------------------

The radius of the cylinder is also r = 3, since each tennis ball fits perfectly in the container.

The height is h = 18 because we have each ball with a diameter 6, which leads to the three of them stacking to 3*6 = 18.

The volume of the cylinder is...

V = pi*r^2*h

V = pi*3^2*18

V = 162pi

-------------------------

Subtract the volume of the cylinder and the combined volume of the spheres:  162pi - 108pi = (162-108)pi = 54pi

This is the exact volume of empty space inside the can.

This points to choice A as the final answer

Pls ASAP Select the correct answer.
What is the sum of this geometric series?

Answers

9514 1404 393

Answer:

  D.  21/2

Step-by-step explanation:

It is probably easiest to add up the three terms.

For n=1, the first term is ...

  8(1/4)^(0) = 8

The second term is ...

  8(1/4)^1 = 2

The third term is ...

  8(1/4)^2 = 8/16 = 1/2

The sum of the series is ...

  8 + 2 + 1/2 = (16 +4 +1)/2 = 21/2

Write the equation of the circle with center C(-5,8) and radius = 7

Answers

Answer:

( h + 5 )^2 + ( y - 8 ) ^2 = 49

Step-by-step explanation:

Equation of a circle:

( x - h )^2 + ( y - k )^2 = r^2

Where ( h , k ) = center and r = radius

We are given that the circle has a center at ( -5 , 8 ) meaning that h = -5 and k = 8

We are also given that the circle has a radius of 7 meaning that r = 7

Now that we have identified each variable we plug the values into the equation

( h - (-5)^2 + ( y - 8 )^2 = 7^2

Our final step is to simplify

we get that the equation of the circle is

( h + 5 )^2 + ( y - 8 ) ^2 = 49

By the way ^ means exponent

The radius of a plant pot is 4.5 cm, and its height is 6 cm. What is the volume of the pot?
Use the value 3.14 for , and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.

Answers

Answer:

381 cm³

Step-by-step explanation:

Volume of the pot = volume of a cylinder

Volume of the pot = πr²h

Where,

π = 3.14

radius (r) = 4.5 cm

h = 6 cm

Substitute

Volume of the pot = 3.14*4.5²*6

Volume of the pot = 381.51 ≈ 381 cm³ (nearest whole number)

Kin travels 440 miles by train at an average speed of 110 mph.
Ayaan flies the same distance at an average speed of 880 mph.
Find the difference between their travel times.
Give your answer in hours.

Answers

Answer:

3 1/2 hours

Step-by-step explanation:

time = distance/speed

440/110 = 4 hours

440/880 = 1/2 hours

4 minus 1/2 is 3 1/2

Answer:

hi

Step-by-step explanation:

i just need some points sorry not sorry

z is a standard normal random variable. The P (1.41 < z < 2.85) equals a.0.4978 b.0.0771 c.0.9185 d.0.4207

Answers

Answer:

[tex]P (1.41 < z < 2.85) = 0.0771[/tex]

Step-by-step explanation:

Required

[tex]P (1.41 < z < 2.85)[/tex]

This is calculated as:

[tex]P (1.41 < z < 2.85) = P(z < 2.85) - P(z < 1.41)[/tex]

From z probabilities:

[tex]P(z < 2.85) = 0.99781[/tex]

[tex]P(z < 1.41) = 0.92073[/tex]

So, we have:

[tex]P (1.41 < z < 2.85) = 0.99781 - 0.92073[/tex]

[tex]P (1.41 < z < 2.85) = 0.07708[/tex]

Approximate

[tex]P (1.41 < z < 2.85) = 0.0771[/tex]

Find the slope of the line through the points (−18,−12) and (0,8).

Answers

Answer:

9/10

Step-by-step explanation:

y2-y1÷x2-x1

-18-0/-12-8

-18/-20

9/10

Answer:10/9

Step-by-step explanation:You do y2-y1 over x^2-x^1 and you get 10/9

What is the answer to this question

Answers

Answer:

its b because when subtract 30-24=6

which rule applies to this equation? (6)(3p) = 18p

Answers

Answer:

multiplication rule

Step-by-step explanation:

because 6 * 3p

is equal to 18p

hope this helps you please like and mark as brainliest

2 show by calculation of nature of triangle AMK
3 CULCULATE BP MK AK

Answers

Answer:

if he is the to form a 666

Step-by-step explanation:

what

I

I

I

want to

be

a

story

about

I

2

2

Express the following repeating decimal as a fraction in simplest form.

Answers

Answer:

[tex]0.\overline{369} = \frac{41}{111}[/tex]

Step-by-step explanation:

x = 0.369369369...

10x = 3.69369369...

100x = 36.9369369...

1000x = 369.369369...

1000x - x = 369

999x = 369

[tex]x = \frac{369}{999} \\\\x = \frac{123}{333}\\\\x = \frac{41}{111}[/tex]

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