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.

The relation f is defined as f(x) = x², 0 ≤ x ≤ 3 3x, 3 ≤ x ≤ 10
It is observed that for 0 ≤ x ≤ 3, we have f(x) = x² and for 3 ≤ x ≤ 10, we have 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
Therefore for every x, 0 ≤ x ≤ 10, we have a unique image under f
Thus, the relation f is a function.
Also, the relation g is defined as g(x) = x², 0 ≤ x ≤ 2 3x, 2 ≤ x ≤ 10
It can be observed that for x = 2, we have g(x) = 2² = 4 and g(x) = 3 × 2 = 6
Thus, the element 2 of the domain of the relation g has two different images i.e., 4 and 6
Hence, this relation is not a function.