Question

State whether the statement given below is true or false. "f:A N, f(n) =prime factor of n is a function, here A = {9, 10, 11, 12,13}."​

Answer 1

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 13×3×1

Highest prime factor of 9 is 3.

Factors of 10 = 2 \times 5 \times 12×5×1

Highest prime factor of 10 is 5.

Factors of 11 = 11 \times 111×1

Highest prime factor of 11 is 11.

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

Highest prime factor of 12 is 3.

Factors of 13 = 13 \times 113×1

Highest prime factor of 13 is 13.

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