Let f(x)= [x/3] (where f(x) is the ceiling function). We learned that the floor and the ceiling functions are NOT invertible, but we also learned about the set of preimages of any value in the Range, the set of images. Keeping that in mind, give your answer in interval notation if necessary.

a. Find f-1({5})
b. Find f-1({-2})
c. Find f-1({x | 5 = x = 9 })
d. Find f-1({x | -6 = x = -2})

Answers

Answer 1

(a) We have ⌊x⌋ = 5 if 5 ≤ x < 6, and similarly ⌊x/3⌋ = 5 if

5 ≤ x/3 < 6   ==>   15 ≤ x < 18

(b) ⌊x⌋ = -2 if -2 ≤ x < -1, so ⌊x/3⌋ = -2 if

-2 ≤ x/3 < -1   ==>   -6 ≤ x < -3

In general, ⌊x⌋ = n if n ≤ x < n + 1, where n is any integer.

I do not understand what is being asked in (c) and (d), so you'll have to clarify...


Related Questions

can help my little bro

Answers

Answer:

$0.03

Step-by-step explanation:

chips: 7.84/16=0.49

pretzels: 12.48/24=0.52

0.52=0.49=0.03


Mark breaks up a 9-hour drive into 3 parts. He drives 2 1/2 hours before stopping for lunch. After driving some more, he stops for gas. If the second part of his drive was 1 2/3 longer than the first part, how long did he drive after stopping for gas?

Answers

Answer:

4 1/6 hours

Step-by-step explanation:

2 1/2 + 1 2/3 = 25/6 = 4 1/6

You want to create an orange color in order to paint the Oriole’s Bird. You have the colors yellow and red to make the orange paint. The recipe for Oriole’s orange paint is 1/2 cup yellow paint to 1/4 cup red paint. Using this ratio:

Part 1: How much yellow paint do you need to combine with one cup of red paint?


Part 2: How much red paint do you need to combine with one cup of yellow paint?

Each snap cube represents 1/4 cup of paint.


Answers

Answer:

Adult males are flame-orange and black, with a solid-black head and one white bar on their black wings. Females and immature males are yellow-orange on the breast, grayish on the head and back, with two bold white wing bars

2a+b+c=9 a+2b+c=8 a+b+2c=11

Answers

[tex] \: \: \: \: \: \: [/tex]

# 2a+b+c=9

answer

[tex]a = \frac{9}{2} - \frac{1}{2} b - \frac{1}{2} c[/tex]

#a+2b+c=8

answer

[tex]a = 8 - 2b - c[/tex]

#a+b+2c=11

answer

[tex]a = 11 - b - 2c[/tex]

refer to the attachment for explanationhope it helps

What is 4/5 divied by 2/5

Answers

Answer:

2

Have a nice day :D

Answer:

2

Hope this helps

07
Question 4
What is the 11th term of the geometric sequence
-1.5, -3, -6, -12, ...? /(5 pts)
Your Answer:

Answers

Answer:

-1536

Step-by-step explanation:

By taking the general formula for the geometric sequence, we substitute the variables with the values of our sequence, finding -1536 as the 11th term

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided
What is the expression in factored form?

2x^2 + 16x + 24

Answers

Solution : 2(+2)(+6)

Explanation : First, look for the common factor; use the sum-product pattern, then for the common factor from the two pairs, lastly, rewrite in factored form.

if h(x) =5 for the function h(x) =2x+1, what is the value of x?
12
11
2​

Answers

Answer:

2

Step-by-step explanation:

5=2x+1

5-1=2x

2x=4

x=2

Answer:

x = 2

Step-by-step explanation:

2x+1 = 5

    -1   -1

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

2x = 4

x = 2

hope this helps! :D

have a miraculous day, and brainliest is immensely appreciated!! <3

80 is the product of Diego's height and 5.
Use the variable d to represent Diego's height.

Answers

Answer: The expression is 5d = 80. 80 ÷ 5 = 16. Therefore, the variable D is 16.

I have a Statistics question​

Answers

Answer:

okayyyyyyyyyyyyyyyy

Step-by-step explanation:

have a nice day

okkkkkkkkkkkkkkkkkkkkkkkk

A fair coin is tossed four times. What is the probability of obtaining at least three tails?

Answers

The probability of obtaining at least three tails is; 5/16

When tossing a coin four times, the number of possibilities since one is either a tail or head is;

Total number of possibilities = 2⁴ = 16

Now, various ways of getting at least three tails are;

TTTH, TTHT, THTT, HTTT, and TTTT.

This is a total of 5 different ways.

Thus;

P(obtaining at least 3 tails) = 5/16

Read more about probability when a coin is tossed at; https://brainly.com/question/1334780

Which choice shows (50+30)+40 correctly written using associative property and then correctly simplified

Answers

Answer:

The first option as you do what is in parentheses first.

Step-by-step explanation:

A restaurant has two sizes of milkshakes, small and regular. The ratio of small milkshakes purchased to regular milkshakes purchased is 14 to 6. What percent of milkshakes purchased are small?

Answers

Answer:

70%

Step-by-step explanation:

the ratio is 14 to 6 so if you have 14 small milkshakes you would also have 6 regular milkshakes

to find a percentage we can buff up the ratio to add up to 100

14 + 6 = 20

100 / 20 = 5

that means we must multiply each side by 5

14 * 5 = 70

6 * 5 = 30

the ratio is now 70 to 30

you would have 70% of milkshakes that are small

Liam cuts a 48-inch piece of string into two pieces. One piece is 12 inches longer than the other. If s represents the length of the shorter string, which diagram best represents this scenario?

Answers

The length of the shorter string is 18 inch while that of the longer string is 30 inch.

An equation is an expression used to show the relationship between two or more variables and numbers.

Let s represent the length of the shorter string.

One piece is 12 inches longer than the other

Length of longer string = s + 12

Since a 48-inch piece of string is cut into two pieces. Hence:

s + (s + 12) = 48

2s + 12 = 48

2s = 36

s = 18

Length of longer string = 18 + 12 = 30

The length of the shorter string is 18 inch while that of the longer string is 30 inch.

Find out more on equation at: https://brainly.com/question/2972832

12 - (8x - 20) < 12
Plz answer question

Answers

[tex]12 - (8x - 20) < 12 <=> 12- 8x+20<12<=> -8x <12-20-12 \\<=>-8x <-20<=>8x>20<=>x>\frac{20}{8}=\frac{5}{2}[/tex]

ANSWER: x > 5/2

Ok done. Thank to me :>

Answer:

[tex]x = \frac{5}{2} [/tex]

Step-by-step explanation:

12-(8x-20)<12

12-8x+20<12

-8x<12-12-20

-8x<-20

divide both by negetive 8

x>5/2

x> 2.5

is 8.5 greater than 0.85?

Answers

Answer:

Yes, 8.5 is greater than 0.85

Step-by-step explanation:

In counting from 0 to the highest possible positive number in steps of 0.01, we come across 0.85 before 8.5. This means that 8.5 is greater than 0.85

CAN SOMEONE HELP ME PLEASE <3

Answers

Answer:

It's Micrograms. The rest are from the imperial system, which is the system that is commonly used in the United States. The metric system is an international system for scientists and mathematicians to use so that sharing and giving information is a lot easier when conveying to other people around the world.

What is the equation of the line that passes through the point (8,6) and has a slope of
{3}{2}

Answers

What is your slope? If you said 3/2 then it would be: y=3/2x-6

If 9 out of 20 candies are orange, how many orange candies will there be per 100 candies total?

Answers

Answer:

45

Step-by-step explanation:

20 / 9 = 2.222222222223

100 / 45 = 2.222222222223

9 is 45% of 20 and 45 is 45% of 100.

6(3x+12-4x)=2x+2+3x solve for x

Answers

Answer:

its 70/11 or 6.36

Step-by-step explanation:

Solve: 5(x+2) = 3x + 5

Answers

Answer:

-2.5

Step-by-step explanation:

5(x+2) = 3x+5

5x+10=3x+5

5x-3x=5-10

2x=-5

x=-2.5

Answer: -5/2

Step-by-step explanation: the explanation and the answer above, -2.5 is correct but it can be simplified to -5/2 for those working in Apex

the sum of three consecutive even numbers is 42. what is the smallest of these numbers

Answers

Explanation :-

Let's assume the lowest integer be x.Then the next integer x+2 (since our integers need to be even) and the third integer x+4.

[tex]\qquad[/tex]____________________

It’s given

The sum of three consecutive even numbers is 42.

[tex] \bf{\underline{\underline{\dag According\ to\ the\ question:-}}} [/tex]

[tex]\qquad[/tex][tex] \pink{\bf\longrightarrow {x+( x +2)+(x+4) = 42} }[/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow 3x +6 =42[/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow 3x = 42-6[/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow 3x =36[/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow x = \cancel {\dfrac{36}{3}}[/tex]

[tex]\qquad[/tex][tex]\pink{ \bf\longrightarrow x = 12}[/tex] ( which is our lowest integer.)

The smallest of these numbers is 12. And the next two integers we find with 12+2=14 and 12+4=16.

[tex]\qquad[/tex]____________________

Given :

Sum of three consecutive even numbers is 42. We are to find the smallest of the smallest consecutive even number.

[tex] \: [/tex]

Solution :

Let us assume the three consecutive even numbers be "x" , "(x + 2)" and "(x + 4)" . Here x is the smallest number .

So,

According to the Question :

x + (x + 2) + (x + 4) = 42

⇢x + x + 2 + x + 4 = 42

⇢ x + x + x + 2 + 4 = 42

⇢ 3x + 6 ⠀⠀⠀⠀⠀ = 42

⇢ 3x ⠀⠀⠀⠀⠀⠀⠀⠀= 42 - 6

⇢ 3x ⠀⠀⠀⠀⠀⠀⠀⠀= 36

⇢ x ⠀⠀⠀⠀⠀⠀⠀⠀= 36/3

⇢ x ⠀⠀⠀⠀⠀⠀⠀⠀ = 12

Hence, 12 is the smallest consecutive even number.

5/50 divided by 15/30 solve it out for me please

Answers

Answer:

1/5

Step-by-step explanation:

First and foremost, I want to simplify these fractions, just to make everything a lot easier when I actually get to dividing. 5/50 can be divided by 5/5 to get 1/10, and 15/30 can be divided by 15/15 to get 1/2. So, now we're dividing 1/10 by 1/2.

To divide fractions, we can multiply the first fraction (in this case, 1/10) by the reciprocal of the second fraction (in this case, 1/2). The reciprocal of 1/2 is 2, so we can multiply 1/10 by 2 to find our answer. 1/10 × 2 = 2/10, or 1/5, so this is our final answer.

Hopefully that's helpful! If you have any further questions, let me know. :)

The quotient of given fractions is 1/5.

Given that, 5/50 divided by 15/30.

What are fractions?

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Now, 5/50 ÷ 15/30

Keep the first fraction 5/50 same change the division symbol and reciprocate the fraction 15/10

That is, 5/50 × 30/15

= 1/10 × 2/1

= 2/10

= 1/5

Therefore, the quotient of given fractions is 1/5.

To learn more about the fractions visit:

https://brainly.com/question/1301963.

#SPJ2

Huilans age is two times Thomas’s age. The sum of their ages is 42. What is Thomas’s age?

Answers

Answer:

14

Step-by-step explanation:

14+28=42, 28/14=2

14 ,, 42/3 !! this is the correct way !

PLS HELP i will mark brainliest

Answers

Set tay equal to x, and set Omar to be equal to y. Then solve for x, which is done simply by dividing both sides by the y value. The answer is your slope

YOU’RE GETTING a brainlist if you answer these!!!!: If you and I meet halfway between the fountain and the restrooms what are the coordinates of our meeting place?

If my cat and your dog meet halfway between the ball field and the swings what are the coordinates of their meeting place?

Now to the nearest yard how far are you and I to our pets after arriving to our meeting place?

Answers

Answer:

Where's the picture?

Step-by-step explanation:

A gumball machine has 240 red gumballs. If the red gumballs are 50% of the total number of gumballs, how many gumballs are in the gumball machine?

Answers

Answer:

480 because 50% is just haf and half has to be equal to the 240 so you just add 240 to 240

Step-by-step explanation:

480
This is because 50% is half of the total. So to find the total, multiply 240 by 2.

Guys please i need help on this, i will give brainliest to the right answers

Answers

Answer:

3x + 3

Step-by-step explanation:

yeah-ya........ right?

When divide f(x)=ax³+bx²+cx+d by (x+3), the remainder is 4, then what is the remainder when divide 2f(x)-6 by (x+3)?​

Answers

Answer:

2

Step-by-step explanation:

When divide f(x)=ax³+bx²+cx+d by (x+3), the remainder is 4:

f(x) = m*(x + 3) + 4, where m is the quotient

Then 2f(x) - 6 is:

2[m(x + 3) + 4] - 6 = 2m(x + 3) + 8 - 6 = 2m(x + 3) + 2

As we see the remainder is 2

A monkey is swinging from a tree, on the first swing, she passes through an arc of 10 m. with each swing she passes through an arc 9/10 the length of the previous swing. what is total distance the monkey has traveled when she completes her 25th swing

Answers

Answer:

≈ 92.821 m

Step-by-step explanation:

For a geometric series with initial value a and rate r, the sum after n terms can be represented by

a*(1-r^n)/(1-r)

Here, we know a = 10 (the first swing), r = 9/10 because the second swing was 9/10 of the first swing, meaning we multiply the first swing by 9/10 to get the second swing, and n = 25. Plugging these values in, we get

10 * (1-0.9^25)/(1-0.9) ≈ 92.821 m

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