The following three functions look very similar, but define very different functions. Think about how they are defined and write each as a composition of functions given the information below. (None of the functions in your compositions should be the same as the given function.) 1. sin^4 (x) = f(g(x)) where f(x) = , and g(x) = . 2. sin(sin(x)) = f(g(x)) where f(x) = , and g(x) = . 3. sin x^4 = f(g(x)) where f (x) = , and g(x) = .

Answers

Answer 1

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following functions :

sin^4 (x) = f(g(x)) where f(x) = and g(x) =

Sin⁴(x) = sin(x)⁴

g(x) = sin(x),

f(x) = f(g(x)) = f(sin(x)⁴) = x⁴

2.) sin(sin(x)) = f(g(x)) where f(x) = , and g(x) =

g(x) = sin(x) ; sinx = x

g(x) = sin(x)

f(x) = f(g(x)) = sin(x) ; sin(x) = x

f(x) = f(g(x)) = f(sin(x))

f(x) = sin(x)

3. sin x^4 = f(g(x)) where f (x) = , and g(x) = .

Here,

g(x) = x⁴

f(x) = f(g(x)) = sin(g(x)) = sin x

f(x) = sinx

Answer 2

The functions are illustrations of composite functions, where multiple functions are combined in one.

(1) sin^4 (x) = f(g(x))

Rewrite the above function as:

[tex]f(g(x)) = \sin^4(x)[/tex]

So, we have:

[tex]f(g(x)) = (\sin(x))^4[/tex]

From the above equation, we have:

[tex]g(x) = \sin(x)[/tex]

So, we have:

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

Substitute x for g(x)

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

Hence, the functions are:  [tex]f(x) = x^4[/tex] and [tex]g(x) = \sin(x)[/tex]

2.) sin(sin(x)) = f(g(x))

Rewrite the above function as:

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

From the above equation, we have:

[tex]g(x) = \sin(x)[/tex]

So, we have:

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

Substitute x for g(x)

[tex]f(x) = \sin(x)[/tex]

Hence, the functions are:  [tex]f(x) = \sin(x)[/tex] and [tex]g(x) = \sin(x)[/tex]

3. sin x^4 = f(g(x))

Rewrite the above function as:

[tex]f(g(x)) = \sin(x^4)[/tex]

From the above equation, we have:

[tex]g(x) = x^4[/tex]

So, we have:

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

Substitute x for g(x)

[tex]f(x) = \sin(x)[/tex]

Hence, the functions are:  [tex]f(x) = \sin(x)[/tex] and [tex]g(x) = x^4[/tex]

Read more about composite functions at:

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Related Questions

Latoya has a 25-pound bag of potting soil. She puts 3 pounds of potting soil in each of f flowerpots. The amount of potting soil that remains can be represented by the expression 25 – 3f.

Answers

Step-by-step explanation:

25 - 3f

25 - 3(7)

25 - 21

4 pounds of potting soil remains

Hope it helps

HELP!!!!! will mark brainliest

Answers

Answer:

its the second and the 3rd one I think

Step-by-step explanation:

Answer:

A and C is correct

Step-by-step explanation:

I hope this helps you :)

-KeairaDickson

(6.2)(5.7) helppp, I need an answer ASAP!
I just don't feel like doing it

Answers

Answer: 35.34

Step-by-step explanation:

(6.2)x(5.7)= 35.34

Hope this helps!

|-3| ×(-6)
hello please​

Answers

Answer:

-18.

Step-by-step explanation:

|-3| = 3.

Hence |-3| * (-6) = 3 * (-6) = -18.

Answer:

the awnser is 18

Step-by-step explanation:

|-3| = 3.

Hence |-3| * (-6) = 3 * (-6) = -18.

Bulbul thinks of a 3-digit number, decreases it by 50 and then increases it by 35. The resulting number will be

Answers

Answer:X-15

Step-by-step explanation:

The variable n represents the number of bikes in a shipping container. The weight of the container in pounds, including the bikes, can be modeled using the expression 250+23(n−1). How much will the container weigh with 20 bikes in it?​

Answers

Answer:

678

Step-by-step explanation:

250 + 23 (20 - 1 )

Replace the n with 20 Bc n is the number of bikes

250 + 23 (20 - 1 )

Do the parentheses

250 + 23 (19)

Multiply the 23 by 19

250 + 437

Add both numbers

The required weight of the 20 bikes in the container is 687 pounds.

An expression regarding relative weight between the bike-containing container is given 250+23(n−1), where n represents the number of bikes and the whole equation gives the cumulative weight of the bikes.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
The given expression is 250+23(n−1),
Now, put n  = 20 According to the question,
Wight  = 250 + 23 (20 - 1)
Weight = 250 + 23 * 19
Weight = 687.

Thus, the required weight of the 20 bikes in the container is 687 pounds.

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What is the length of DT where D(-6-2) and T(7-8)

Answers

Answer:

[tex] d = \sqrt{205} [/tex]

Step-by-step explanation:

[tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

[tex] d = \sqrt{(-8 - (-2))^2 + (7 - (-6))^2} [/tex]

[tex] d = \sqrt{(-6)^2 + 13^2} [/tex]

[tex] d = \sqrt{36 + 169} [/tex]

[tex] d = \sqrt{205} [/tex]

Answer:

√205

Step-by-step explanation:

Plug into distance formula

Expand the expression (x-5)^3

Answers

x^3 - 15x^2 + 75x - 125

Answer:

[tex]x^3[/tex]-15[tex]x^{2}[/tex]+25x-125

Step-by-step explanation:

This is a quadratic equation, so we need to open the equation first. There are three (x-5), and then we multiply them together, and then combine like terms to get the answer.

(x-5)(x-5)(x-5)=

[x(x-5)-5(x-5)](x-5)=

([tex]x^{2}[/tex]-5x-5x+25)(x-5)=

([tex]x^{2}[/tex]-10x+25)(x-5)=

x([tex]x^{2}[/tex]-10x+25)-5([tex]x^{2}[/tex]-10x+25)

[tex]x^3[/tex]-[tex]10x^2[/tex]+25x-[tex]5x^2[/tex]-125=

[tex]x^3[/tex]-15[tex]x^{2}[/tex]+25x-125

The difference between a number 12 is 20

Answers

Answer:

If you mean "the difference between a number AND 12 is 20" the x-12=20

Step-by-step explanation:

"difference" means subtraction and "and" indicates where that sign goes. "is" means "=".

help ;-;

A mechanic charges $168 for parts and $35 per hour for labor. Write an expression for the total charge. Evaluate the expression to find the total charge for 3 hours of labor.​

Answers

Answer:

35(3)+168= 278

Step-by-step explanation:

35(x)+168

x= the hours of labor

Round 34,971.22 to the hundreds place.

Answers

Answer:

35000

Step-by-step explanation:

Since all numbers above 50 round to a hundred, we see that the number 34,971.22 has the tens digit over 5. We can then round this to 35,000.

if i have 2 dogs and 3 cats how many animals do i have

Answers

Then you have five animals

Answer:

5 animals

Step-by-step explanation:

2 + 3 = 5

hope this helps you :)

can you friend me again I accidentally unfriended you  :)

pls mark me brainlest ;)

A basketball player makes 60% of his free throws. We set him on the line of free-throw and informed him to shoot free throws until he misses. Let the random variable X be the number of free throws taken by the player until he misses. Assuming that his shots are independent, find the probability that he will miss the shot on his 6th throw. Show work detail please
a) 0.04666
b) 0.03110
c) 0.01866
d) 0.00614

Answers

Answer:

B. 0.03110

Step-by-step explanation:

Given

Probability of Hit = 60%

Required

Determine the probability that he misses at 6th throw

Represent Probability of Hit with P

[tex]P = 60\%[/tex]

Convert to decimal

[tex]P = 0,6[/tex]

Next; Determine the Probability of Miss (q)

Opposite probabilities add up to 1;

So,

[tex]p + q = 1[/tex]

[tex]q = 1 - p[/tex]

Substitute 0.6 for p

[tex]q = 1 - 0.6[/tex]

[tex]q = 0.4[/tex]

Next,is to determine the required probability;

Since, he's expected to miss the 6th throw, the probability is:

[tex]Probability = p^5 * q[/tex]

[tex]Probability = 0.6^5 * 0.4[/tex]

[tex]Probability = 0.031104[/tex]

Hence;

Option B answers the question

Answer:

b) 0.03110

Step-by-step explanation:

Got it right on the test.

1, 5, 14, 30, 55, __,__

Answers

Answer:

91, 140

Step-by-step explanation:

hope this helps

Write the set of real numbers between 110 and 220 in interval notation.

Answers

Answer:

[tex]110\geq x \leq 220[/tex]

Step-by-step explanation:

Given

Minimum: 110

Maximum = 220

Required

Write as interval notation

Let the real numbers be represented with x

We start by setting x greater than or equal to the minimum:

[tex]x \geq 110[/tex]

Then, we set x less than or equal to the maximum:

[tex]x \leq 220[/tex]

Write out both inequalities

[tex]x \geq 110[/tex] and [tex]x \leq 220[/tex]

This can be rewritten as:

[tex]110 \geq x[/tex] and [tex]x \leq 220[/tex]

Both inequalities can be merged to give:

[tex]110\geq x \leq 220[/tex]

Answer:

(110,220)

I not sure about this answer but if I correct than your welcome and if I wrong then sorry.

Solve the equation using the Properties of Equality.
1/5y+1/8=1/5 y=

Answers

Explanation:


Answer: 3/8

What is 7m + 3mn when m=8 and n=14 I need answers now

Answers

Answer:

392

Step-by-step explanation:

7(8) + 3(8)(14)

56 + 24(14)

56 + 336

392

Answer:

392.

Step-by-step explanation:

7m + 3mn Substitute the variables.

7(8) + 3(8)(14) Multiply from left to right.

56 + 24*14 Multiply 24 by 14.

56 + 336 Add the products.

392 is the answer.

18=3(3x-6) multi step equation

Answers

Answer:

x=4

Step-by-step explanation:

18=3(3x-6)

Divide each side by 3

18/3=3/3(3x-6)

6 = 3x-6

Add 6 to each side

6+6 = 3x-6+6

12 = 3x

Divide by 3

12/3 = 3x/3

4 =x

Jacob needs 48 ounces of tomatoes for the spaghetti sauce he is choosing between the two brands shown explain how Jacob can determine which is the better value

Answers

Answer:Jacob could compare the unit rates of cost per ounce. The unit rate that is less per ounce is the better deal. Not He can look at the cost per ounces!

Im late but hope this helps anyone doing makeup work!

Brand A costs $0.37 or 37 cents per ounce and Brand B costs $0.31 or 31 cents per ounce.

We need to find the unit rate for each brand. Round to the nearest cent (hundredth).

What are ounces?

The definition of an ounce is 1/16 of a pound or a very small amount of something.

According to column 1, 8 ounces of tomatoes would cost 2 dollars and 99 cents. So, the cost of one ounce of tomatoes can be calculated as follows.

When the cost of one ounce of tomatoes is rounded off to the nearest cent, it can be written as $0.37.

According to column 2, 16 ounces of tomatoes would cost 4 dollars and 99 cents. So, the cost of one ounce of tomatoes can be calculated as follows.

When the cost of one ounce of tomatoes is rounded off to the nearest cent, it can be written as $0.31.

Therefore, Brand A costs $0.37 or 37 cents per ounce and Brand B costs $0.31 or 31 cents per ounce.

To learn more about the ounces visit:

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Complete question:

Jacob needs 48 ounces of tomatoes for the spaghetti sauce. He is choosing between two brands of tomatoes.

A 2-column table with 2 rows. Column 1 is labelled Brand A with entries 8 ounces, 2 dollars and 99 cents. Column 2 is labeled brand B with entries 16 ounces, 4 dollars and 99 cents.

Find the unit rate for each brand. Round to the nearest cent (hundredth).

Brand A costs

per ounce.

Brand B costs

per ounce.

I’m so stuck on this , can someone please help ?

Answers

Answer:

see attached.

Step-by-step explanation:

Solve for : x= 2x+15

Answers

Answer:

x = 2x + 15

x - 2x = 2x +15

-x = 15

-x /- = 15/-

x = -15

Step-by-step explanation:

hope that will help you.

Answer:

x = −15

Step-by-step explanation:

x−2x = 2x+15−2x

−x = 15

−x/−1 = 15/−1

x = −15

The absolute value of a number is​

Answers

Answer:

The absolute value of a number is always positive. So that means you circled the correct one. GOOD JOB!!!!!!!!!!!!!!!!!!!!!!!

Step-by-step explanation:

absolute value will always be positive

Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determine two values of xx that support your conclusion. x+8= x+8= \,\,8+x 8+x

Answers

Answer:no solution because it will equal 0

tep-by-step explanation:

What is the domain of the given function
{(3,-2),(6,1),(-1,4),(5,9),(-4,0)}

Answers

The answer is

{x|x= -4, -1, 3, 5, 6}

Hope this helps!!

Solve the equation using the distributive property and properties of equality. Negative 5 (a + 3) = negative 55 What is the value of a? Negative 14 Negative 8 8 14

Answers

Answer:

The answer is C.8. The answer above is incorrect.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

on edge 2021

I need to find f(-2) in this graph however I don't know please help me

Answers

Answer:  1

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

Explanation:

Check out the diagram below. Locate -2 on the horizontal x axis. Draw a vertical line through this value. Mark where the vertical line crosses the curve. Call this point P. Then draw a horizontal line through point P to have it cross the y axis. This horizontal line crosses at y = 1

In short, x = -2 leads to y = 1

So that is why f(-2) = 1

This is another way of saying f(x) = 1 when x = -2.

Note: y = f(x) since both are outputs of a function

Evaluate the expression:

(5/7)³ = ?​

Answers

Answer:

125 over 343 as a fraction and 0.364431 as a decimal

Step-by-step explanation:

hope this helps dont know if its right

Answer:

125/343

Step-by-step explanation:

I am horrible at algebra its just not made for me to understand

Answers

formula: A=bh

A=72

b=12

72=12h

h=72/12

h=6

im so comfused please help​

Answers

Answer:

it is graph b , but im very sorry if yu  get it wrong mb:) i tried:)

Step-by-step explanation:

Is a cross section 2 dimensional figure or three-dimensional figure?

Answers

Answer: It is a three-dimensional figure

Step-by-step explanation:

All figures that I have seen cross-section are only three-dimensional figures because it has volume.

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