(i) Given relation is f (x) = $\begin{cases} x^2, & 0 \le x \le 3 \\ 3x, & 3 \le x \le 10 \end{cases}$ Here f (x) = $x^2$ for all x ∈ [0, 3] ⇒ f(3) = $3^2$ = 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) = $\begin{cases} x^2, & 0 \le x \le 2 \\ 3x, & 2 \le x \le 10 \end{cases}$ Here, g(x) = $x^2$ ∀ x ∈ [0, 2] ⇒ g(2) = $2^2$ = 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.