# NCERT Class 11 Mathematics Solutions: Chapter 2 –Relations and Functions Miscellaneous Exercise Part 1

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1. The relation is defined by

The relation is defined by

Show that f is a function and g is not a function.

Answer:

The relation is defined as

It is observed that for

,

Also, at

i.e., at

Therefore, for , the images of are unique.

Thus, the given relation is a function.

The relation g is defined as

It can be observed that for and also

Hence, element of the domain of the relation corresponds to two different images i.e., 4 and 6.

Hence, this relation is not a function.

2. If , find

Answer:

3. Find the domain of the function

Answer:

The function is,

It can be seen that function is defined for all real numbers except at and .

So, the domain of is .