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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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Vesnalui [34]

Michael took the return trip at a velocity 33.75 miles per hour.

<h3>How fast did Michael drive in his return trip?</h3>

Let suppose that Michael drove in <em>straight line</em> road and at <em>constant</em> velocity. Therefore, the speed of the vehicle (v), in miles per hour, can be defined as distance traveled by the vehicle (d), in miles, divided by travel time (t), in hours.

First trip

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Second trip

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By (1) and (2):

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Michael took the return trip at a velocity 33.75 miles per hour.

To learn more on velocities: brainly.com/question/18084516

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2 years ago
Please answer ASAP WILL GIVE BRAINIEST (PLEASE NO SPAM ANSWERS)
Alexeev081 [22]

There are 11 trains containing giraffes and 7 trains containing rabbits.

<h3>Equation</h3>

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

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A possible solution is x = 11, y = 7

There are 11 trains containing giraffes and 7 trains containing rabbits.

Find out more on Equation at: brainly.com/question/22688504

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