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Mamont248 [21]
3 years ago
15

Let f(x)= [x/3] (where f(x) is the ceiling function). We learned that the floor and the ceiling functions are NOT invertible, bu

t 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})
Mathematics
1 answer:
meriva3 years ago
8 0

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

5 ≤ <em>x</em>/3 < 6   ==>   15 ≤ <em>x</em> < 18

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

-2 ≤ <em>x</em>/3 < -1   ==>   -6 ≤ <em>x</em> < -3

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

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

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pickupchik [31]

Answer:

16

Step-by-step explanation:

f ( x ) = 3x² - 2x

To find : f ( - 2 )

f ( - 2 ) = f ( x )

Here,

x = - 2

f ( - 2 ) = 3 ( - 2 )² - 2 ( - 2 )

           = 3 ( 4 ) - 2*( - 2 )

           = 3*4 + 4

           = 12 + 4

f ( - 2 ) = 16

8 0
2 years ago
25. Which word does NOT describe the set of points? (1,5) (2, 2) (3, -1) (4,-4) (5, -7) (6,-10) Decreasing Function Increasing L
egoroff_w [7]

Answer:

it would be decreasing

Step-by-step explanation:

because it is a linear increasing function

for 1 it is going up from 1-6

and 2 it is a function because there isn't any multiples of the x values/ inputs that go to one y value/ output.

7 0
2 years ago
A diver dives from the board at a local swimming pool. Her height, y, in metres, above the water in terms of her horizontal dist
Aneli [31]

Answer:

4 meters

Step-by-step explanation:

Given a quadratic equation in which the coefficient of x^2 is negative, the parabola opens up and has a maximum point. This maximum point occurs at the line of symmetry.

Since the divers height, y is modeled by the equation

y= -x^2 + 2x + 3

Step 1: Determine the equation of symmetry

In the equation above, a=-1, b=2, c=3

Equation of symmetry, x=-\dfrac{b}{2a}

x=-\dfrac{2}{2*-1}\\x=1

Step 2: Find the value of y at the point of symmetry

That is, we substitute x obtained above into the y and solve.

y(1)= -1^2 + 2(1) + 3=-1+2+3=4m

The maximum height of the diver is therefore 4 meters.

8 0
3 years ago
Teesha is in the French club. There are 29 students in the club. The French teacher will pick two students at random to guide vi
Makovka662 [10]
Probability of event A ( Tesha will not be picked as a guide ) :
P ( A ) = Number of ways it can happen / Total number of outcomes
P ( A ) = (29 - 2) / 29 = 27 / 29 ≈ 0.93
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The probability that Tesha will not be picked as a guide is 0.93 or 93 %. 
5 0
3 years ago
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What is the ratio of 267?
Dmitry [639]
The answer is 133.5 I got this by dividing 267 by 2
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