Let A = \{7, 8, 9, 10, 11, 12, 13, 14, 15, 16\} and let f:A\rightarrow N be defined by f(x) = the highest prime factor of x. How many elements are there in the range of f?
- A. 4
- B. 5
- C. 6 ✓
- D. 7
Correct Answer: C. 6
Explanation
Calculating f(x) for each element: f(7)=7, f(8)=2, f(9)=3, f(10)=5, f(11)=11, f(12)=3, f(13)=13, f(14)=7, f(15)=5, f(16)=2. The unique values in the range are \{2, 3, 5, 7, 11, 13\}. There are 6 elements in the range.
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