#### 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*.

#### Solution

A = {9, 10, 11, 12, 13}

*f*: A → **N** is defined as

*f*(*n*) = The highest prime factor of *n*

Prime factor of 9 = 3

Prime factors of 10 = 2, 5

Prime factor of 11 = 11

Prime factors of 12 = 2, 3

Prime factor of 13 = 13

∴*f*(9) = The highest prime factor of 9 = 3

*f*(10) = The highest prime factor of 10 = 5

*f*(11) = The highest prime factor of 11 = 11

*f*(12) = The highest prime factor of 12 = 3

*f*(13) = The highest prime factor of 13 = 13

The range of *f* is the set of all *f*(*n*), where *n* ∈ A.

∴Range of *f* = {3, 5, 11, 13}

Is there an error in this question or solution?

Solution 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. Concept: Functions.