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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]

Answer:

0.3101001000......

0.410100100010000....

Step-by-step explanation:

To find irrational number between any two numbers, we first need to understand what a rational and irrational number is.

Rational number is any number that can be expressed in fraction of form p/q. Since q can be 1, all numbers that terminate are rational numbers. Example: 1, 12.34, 123.66663

Irrational number on the other hand can't be expressed as a fraction and do not terminate. Also, there is no pattern in numbers i.e. there is no repetition in numbers after the decimal point.

For example: 3.44444..... can be expressed as rational number 3.45.

But 3.414114111.... is an irrational number as there no pattern observed. Also,it does not terminate.

We can find infinite number of irrational numbers in between two rational numbers.

<u>Irrational numbers in between 0.3 and 0.7:</u>

0.3101001000......

0.410100100010000....

0.51010010001.......

0.6101001000....

There are many others. We can choose any two as answers.


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