The relation f is defined by f (x) = {x², 0 ≤ x ≤ 3; 3x, 3 ≤ x ≤ 10}
The relation g is defined by g (x) = {x², 0 ≤ x ≤ 2; 3x, 2 ≤ x ≤ 10}
Show that f is a function and g is not a function

Solution:

The relation f is defined as f (x) = {x², 0 ≤ x ≤ 3; 3x, 3 ≤ x ≤ 10}

It can be observed that for

0 < x < 3, f (x) = x² and

3 < x ≤ 10, f (x) = 3x

Also, at x = 3

f (x) = x² = 9

and f (x) = 3 x 3 = 9

i.e., at x = 3, f (x) = 9

Therefore, for 0 ≤ x ≤ 10,

the images of f (x) are unique.

Thus, the given relation is a function.

The relation g is defined as g (x) = {x², 0 ≤ x ≤ 2; 3x, 2 ≤ x ≤ 10}

It can be observed that for

0 ≤ x ≤ 2, g (x) = x² and

2 ≤ x ≤ 10, g (x) = 3x

Also, at x = 2

g (x) = 2² = 4

and g (x) = 3 x 2 = 6

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

Hence, this relation is not a function.

Thus, f is a function and g is not a function.

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NCERT Solutions Class 11 Maths Chapter 2 Exercise ME Question 1

The relation f is defined by f (x) = {x², 0 ≤ x ≤ 3; 3x, 3 ≤ x ≤ 10} The relation g is defined by g (x) = {x², 0 ≤ x ≤ 2; 3x, 2 ≤ x ≤ 10} Show that f is a function and g is not a function

Summary:

A relation f is defined by f (x) = {x², 0 ≤ x ≤ 3; x, 3 ≤ x ≤ 10} and relation g is defined by g (x) = {x², 0 ≤ x ≤ 2; 3x, 2 ≤ x ≤ 10} is given. We have found that f is a function and g is not a function