NCERT Class 11 Mathematics Solutions: Chapter 2 –Relations and Functions Miscellaneous Exercise Part 1
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Condition of a Function
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 .