# NCERT Class 11 Mathematics Solutions: Chapter 2 – Relations and Functions Miscellaneous Exercise Part 4 (For CBSE, ICSE, IAS, NET, NRA 2023)

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1. Let be the subset of defined by . Is a function from : justify your answer.

Answer:

The relation f is defined as

We know that a relation from a set to a set is said to be a function if every element of set has unique images in set .

Since

i.e.. ,

It can be seen that the same first element i.e.. , corresponds to two different images i.e.. , and .

Relation f is not a function.

3. Let and let be defined by the highest prime factor of . Find the range of .

Answer:

is defined as The highest prime factor of

Prime factor of

Prime factors of

Prime factor of

Prime factors of

Prime factor of

The highest prime factor of

The highest prime factor of

The highest prime factor of

The highest prime factor of

The highest prime factor of

The range of is the set of all , where

Range of