Question

let a={9,10,11,12,13} find f:A to N defined by f(n)=the highest prime factor of n.find the domain and range of f​

Answer 1

using definition of domain and range.

Answer 2

The domain of f is {9, 10, 11, 12, 13}

The range of f is {3, 5, 11, 13}.

Step-by-step explanation:

We are given that A = {9,10,11,12,13} and f: A to N defined by f(n) = the highest prime factor of n.

Firstly, the set A = {9, 10, 11, 12, 13}

and it is sure that n ∈ A = {9, 10, 11, 12, 13}. This means that the domain of the function f is the set A itself {9, 10, 11, 12, 13}.

Now, for finding the range of the function, we have to find the prime factors of each and every value stated in set A.

Factors of 9 = $3 \times 3 \times 1$

Highest prime factor of 9 is 3.

Factors of 10 = $2 \times 5 \times 1$

Highest prime factor of 10 is 5.

Factors of 11 = $11 \times 1$

Highest prime factor of 11 is 11.

Factors of 12 = $2 \times 2 \times 3 \times 1$

Highest prime factor of 12 is 3.

Factors of 13 = $13 \times 1$

Highest prime factor of 13 is 13.

So, the range of the function f is {3, 5, 11, 13}.