During the festival season, there was a mela organized by the Resident Welfare Association at a park, near the society. The main attraction of the mela was a huge swing installed at one corner of the park. The swing is traced to follow the path of a parabola given by $x^2 = y$. Based on the above information, answer the following questions : (i) Let $f: \mathbb{N} \longrightarrow \mathbb{R}$ is defined by $f(x) = x^2$. What will be the range ? (ii) Let $f: \mathbb{N} \longrightarrow \mathbb{N}$ is defined by $f(x) = x^2$. Check if the function is injective or not. (iii) (a) Let $f: \{1, 2, 3, 4 .....\} \longrightarrow \{1, 4, 9, 16 .....\}$ be defined by $f(x) = x^2$. Prove that the function is bijective. OR (iii) (b) Let $f: \mathbb{R} \longrightarrow \mathbb{R}$ is defined by $f(x) = x^2$. Show that $f$ is neither injective nor surjective.