The relation f is defined by 

The relation g is defined by 

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

Asked by Abhisek | 11 months ago |  106

1 Answer

Solution :-

The given relation f is defined as:

It is seen that, for 0 ≤ x < 3,

f(x) = xand for 3 < x ≤ 10,

f(x) = 3x

Also, at x = 3

f(x) = 32 = 9 or f(x) = 3 × 3 = 9

i.e., at x = 3, f(x) = 9 [Single image]

Hence, for 0 ≤ x ≤ 10, the images of f(x) are unique.

Therefore, the given relation is a function.

Now,

In the given relation g is defined as

It is seen that, for x = 2

g(x) = 22 = 4 and g(x) = 3 × 2 = 6

Thus, element 2 of the domain of the relation g corresponds to two different images i.e., 4 and 6.

Therefore, this relation is not a function.

Answered by Pragya Singh | 11 months ago

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