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ipn [44]
2 years ago
6

ion:-}" alt="\large\sf\fbox\red{Question:-}" align="absmiddle" class="latex-formula">
check the injectivity and subjectivity of the function:

\sf \large f:N \longmapsto \: N \: given \: by \: f(x) = x {}^{3} .​
Mathematics
2 answers:
tamaranim1 [39]2 years ago
6 0

Answer:

  • The function is injective but nor surjective

Step-by-step explanation:

<u>We see that:</u>

  • f(x) = x³

<u>For any x₁ and x₂ ∈ N, </u>

  • f(x) = x₁³ = x₂³ ⇒ x₁ = x₂, both are natural numbers

It it confirmed one-to-one, hence it is injective

<u>Check the surjectivity:</u>

f(x) = y ∈ N

  • x³ = y
  • y = ∛x

<u>Let y = 2, then:</u>

  • 2 = x³
  • x = ∛2 ∉ N

Since x is not natural, the function is not surjective

matrenka [14]2 years ago
3 0

Answer:

This function is injective only.

Step-by-step explanation:

N = natural numbers = positive whole numbers equal to or greater than 1.

Therefore N \rightarrow N means that both the input and output are natural numbers.

A function is surjective if for every element in the codomain, there is at least one element in the domain.

Therefore, this function is NOT surjective.  For example, there is no natural number for x for which f(x) = 2.

A function is injective if for every element in the codomain, there is at <u>most</u> one element in the domain.  This is also called "One-to-One".

Therefore, this function IS injective as there is either none or only one value of x for each value in the codomain.

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Please help out with some of these.
nikdorinn [45]

Answer:

1. 1/12

2. 1/8

3. 1/6

4. 1/6

5. 1/4

6. 1/8

7. 1/6

8. 1/8

9. 1/12

Step-by-step explanation:

6 0
3 years ago
12) Given f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}
never [62]

Answer:

<em>Part a) </em>Domain of f : {-3, -2, -1, 0, 1, 2, 3}

<em>Part b) </em>Domain of g : {-1, 0, 1, 2, 3, 4}

<em>Part c)  </em>Domain of f+g = {-1, 0, 1, 2, 3}

<em>Part d) </em>Ordered Pairs of f-g = {(-1, 10), (0, 2), (1, -2), (2, 4), (3, 23)}

Step-by-step explanation:

<em>Part a) Determining the domain of f </em>

Given f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

Domain is the set of the input values of x which define the function. In other words, domain is the set of all the first elements of order pairs.

Domain of f : {-3, -2, -1, 0, 1, 2, 3}

<em>Part b) Determining the domain of g</em>

Given g= {(-1,4),(0,5),(1,6),(2,1),(3,-16),(4,-51)}

As domain is the set of the input values of x which define the function. In other words, domain is the set of all the first elements of order pairs.

Domain of g : {-1, 0, 1, 2, 3, 4}

<em>Part c) Determining the domain of f+g</em>

<em>When there is a sum of two functions f and g, then domain of f+g will be the intersection of their domains.</em>

<em>As,</em>

<em>      </em>Given f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

      Domain of f : {-3, -2, -1, 0, 1, 2, 3}

and,

      Given g= {(-1,4),(0,5),(1,6),(2,1),(3,-16),(4,-51)}

       Domain of g : {-1, 0, 1, 2, 3, 4}

<em>As</em> when <em>there is a sum of two functions f and g, then domain of f+g will be the intersection of their domains</em>

So, the domain of f+g = {-1, 0, 1, 2, 3}

<em>Part d) List the ordered pairs of f-g</em>

As

    f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}

and

    g = {(-1,4),(0,5),(1,6),(2,1),(3,-16),(4,-51)}

For f - g, we must focus on subtracting the second (y) coordinates of both function that correspond to the same element in the domain (x)

(f - g)(x) = f(x) - g(x)

(f - g)(x) = f(-1) - g(-1)  = 14 - 4 = 10

(f - g)(x) = f(0) - g(0)  = 7 - 5 = 2

(f - g)(x) = f(1) - g(1)  = 4 - 6 = -2

(f - g)(x) = f(2) - g(2)  = 5 - 1 = 4

(f - g)(x) = f(3) - g(3)  = 7 - (-16) = 23

So,

Ordered Pairs of f-g = {(-1, 10), (0, 2), (1, -2), (2, 4), (3, 23)}

Keywords:  domain, function, f+g, f-g

Learn more about domain, and ordered pairs from brainly.com/question/11422136

#learnwithBrainly

7 0
3 years ago
Solve for x: 3x-2&gt;5x+10
Pani-rosa [81]

Combine like terms:


3x-2>5x+10 becomes -12 > 2x


Dividing both sides by 2, we obtain x < -6

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3 years ago
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Jerry ran 3/4 of a mile in 1/8 of an hour. What was Jerry's rate of speed in miles per hour?
yarga [219]

Answer:

6 miles per hour

Step-by-step explanation:

we'll set up the problem like this:

3/4 mi = 1/8 hr

now multiply each side by 8:

24/4 mi = 1 hr

simplify:

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3 0
3 years ago
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Find the distance between points P(8,1) and Q(1,6) to the nearest tenth
Ronch [10]
1 - 8 = - 7
6 - 1 = 5

Let us use the Pythagorean theorem:

c^2 = (-7)^2 + 5^2 = 49 + 25 = 74 -> c = 8.6
5 0
2 years ago
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