Given:
A = {9, 10, 11, 12, 13}
f : A → N defined by
f(n) = highest prime factor of n
Step 1: Find f(n) for each element of A
n = 9
9 = 3 × 3
Highest prime factor = 3
f(9) = 3
n = 10
10 = 2 × 5
Highest prime factor = 5
f(10) = 5
n = 11
11 is a prime number
Highest prime factor = 11
f(11) = 11
n = 12
12 = 2 × 2 × 3
Highest prime factor = 3
f(12) = 3
n = 13
13 is a prime number
Highest prime factor = 13
f(13) = 13
Step 2: Write the range of f
Range of f = {3, 5, 11, 13}
Final Answer:
The range of the function f is {3, 5, 11, 13}.