(i) Given relation is
f (x) = {

x2	0≤x≤3
3x	3≤x≤10

Here f (x) = x2 for all x ∈ [0, 3] ⇒ f(3) = 32 = 9
and f (x) = 3x for all x ∈ [3, 10] ⇒ f(3) = 3 × 3 = 9.
It shows that f (x) takes unique value at each point in its domain [0, 10].
Hence, f (x) is a function.
(ii) Given relation is
g (x) = {

x2	0≤x≤2
3x	2≤x≤10

Here, g(x) = x2 ∀ x ∈ [0, 2]
⇒ g(2) = 22 = 4 and g(x) = 3x ∀ x ∈ [2, 10] ⇒ g(2) = 3 × 2 = 6
It shows that g(x) does not take unique value at point 2. Hence, g(x) is not a function.