Question

Let A = {9, 10, 11, 12, 13} and let f : A → N be defined by f ( n ) = the highest prime factor of n . Find the range of f .

Answer 1

Let set A={ 9,10,11,12,13 }and f( x ):A→N, f( n ) is the highest prime factor.

The prime factor of set Ais calculated as,

Prime factor of ( 9=3×3 )is 3 and the highest prime factor of 9 is f( 9 )=3.

Prime factor of ( 10=2×5 )is 2,5 and the highest prime factor of 10 is f( 10 )=5.

Prime factor of ( 11=1×11 )is 11 and the highest prime factor of 11 is f( 11 )=11.

Prime factor of ( 12=2×2×3 )is 2, 3 and the highest prime factor of 12 is f( 12 )=3.

Prime factor of ( 13=1×13 )is 13and the highest prime factor of 13 is f( 13 )=13.

The range of function is the set of all f( n ).

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