# NCERT Class 11 Mathematics Solutions: Chapter 2 – Relations and Functions Miscellaneous Exercise Part 2 (For CBSE, ICSE, IAS, NET, NRA 2022)

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1. Find the domain and range of the real function define by .

The given real function is .

It can be seen that is defined for

i.e.. , is defined for

So, the domain of is the set of all real numbers greater than or equal to i.e.. , the domain of

As,

So, the range of is the set of all real numbers greater than or equal to

i.e.. , the range of .

2. Find the domain and the range of the real function f defined by .

The given real function is .

It is clear that is defined for all real numbers.

∴ Domain of

Also, for assumes all real numbers.

So, the range of is the set of all non-negative real numbers.

3. Let be a function from into . Determine the range of .

The range of is the set of all second elements.

It can be observed that all these elements are greater than or equal to 0 but less than .

[ Denominator is greater numerator] Thus, range of

3. Let be defined, respectively by , . Find

, and .