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3 years ago

I need help with this problem and I need it today

Mathematics

1 answer:

ANTONII [103]3 years ago

6 0

Answer:

2d shape and the area is i think 3

Step-by-step explanation:

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Determine whether each of these functions from Z to Z is one-to-one. a) f(n) = n - 1 b) f(n) = n2 + 1 c) f(n) = nº d) f(n) = [n/

sesenic [268]

Answer: The correct option is

(a) f(n) = n - 1.

Step-by-step explanation: We are given to determine whether the given functions are one-to-one or not.

We know that a function y = f(x) is one-to-one if and only if

f(x) = f(y) ⇔ x = y.

That is, any two distinct elements cannot have the same image.

(a) The given function is

$f(n)=n-1.$

Let us consider that

$f(n_1)=f(n_2)\\\\\Rightarrow n_1-1=n_2-1\\\\\Rightarrow n_1=n_2.$

Similarly,

$n_1=n_2\\\\\Rightarrow n_1-1=n_2-1\\\\\Rightarrow f(n_1)=f(n_2).$

So, this function is one-to-one.

(b) The given function is

$f(n)=n^2+1.$

Let us consider that

$f(n_1)=f(n_2)\\\\\Rightarrow n_1^2+1=n_2^2+1\\\\\Rightarrow n_1^2=n_2^2\\\\\Rightarrow n_1=\pm n_2.$

That is, there may be two unequal elements having same image.

For example, f(-1)=(-1)²+1=1+1=2, f(1)=(1)²+1=1+1=2.

It implies that f(-1)=f(1) but 1 ≠ -1.

So, the given function is not one-to-one.

(c) The given function is

$f(n)=n^0.$

Here, the image of all the elements is 1.

For example, $f(2)=2^0=1,~~f(3)=3^0=1.$

f(2)=f(3) but 2≠3.

So, more than one element is having the same image and so the function cannot be one-to-one.

(d) The given function is

$f(n)=\left[\dfrac{n}{2}\right].$

Here, we see that

$f(2)=\left[\dfrac{2}{2}\right]=[1]=1,\\\\\\f(3)=\left[\dfrac{3}{2}\right]=[1.5]=1.$

So, f(2)=f(3) but 2≠3.

So, the given function is not one-to-one.

Thus, the correct option is (a).

5 0

4 years ago

A monopolist's marginal cost curve shifts up, but the firm's demand curve remains the same and the firm does not shut down. Comp

Stells [14]

Answer:

(1)raise, (2)decrease

Step-by-step explanation:

A monopolist's marginal cost curve shifts up, but the firm's demand curve remains the same and the firm does not shut down. Compared with the condition before the increase in marginal costs, the monopolist will raise its price and decrease its level of production.

Marginal cost is the additional cost incurred when one more unit of the output is produced. It is a J-shaped curve, which initially decreases, reaches its minimum and then starts increasing.

Marginal cost is an important factor in economic theory because a company that is looking to maximize its profits will produce up to the point where marginal cost (MC) equals marginal revenue

6 0

3 years ago

A rectangular garden 50 feet long and 10 feet wide is enclosed by a fence. To make the garden larger, while using the same fence

ivann1987 [24]

The area of the rectangular garden is 50 x 10 = 500 square feet.

The perimeter of the rectangular garden is 50 + 50 + 10 +10 =120 feet.

The perimeter of the square also needs to be 120 because it is using the same amount of fence.

Divide 120 by 4 sides: 120/4 = 30

Each side of the square garden would need to be 30 feet.

The area of a square is Side^2, 30^2 = 900 square feet.

The square is 900 - 500 = 400 square feet more.

3 0

3 years ago

Read 2 more answers

What is the vertex of f(x)=x2−8x+15 ?

mr_godi [17]

Answer:

(4,-1)

i strongly believe that is the answer, pls mark as brainlist

4 0

3 years ago

The sum of a number and 9, divided by 4, is greater than or equal to -2

Sidana [21]

Answer:y – 9. 4 less than a number. y - 4

Step-by-step explanation:

8 0

3 years ago

I need help with this problem and I need it today​

I need help with this problem and I need it today