# NCERT Class 11 Mathematics Solutions: Chapter 2 –Relations and Functions Miscellaneous Exercise Part 2

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

Answer:

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 .

Answer:

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 .

Answer:

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 .

Answer:

,

where,

Where,