CASE STUDY CHALLENGE
Relations & Functions: The Festival Swing
During the festival season, there was a mela organized by the Resident Welfare Association at a park. The main attraction was a huge swing installed at one corner of the park. The swing is traced to follow the path of a parabola given by x2 = y.
∪
Parabolic Path y = x2
Answer the following:
| (i) | Let f : N → R be defined by f(x) = x2. What will be the range? | [1] |
| (ii) | Let f : N → N be defined by f(x) = x2. Check if the function is injective or not. | [1] |
| (iii) | (a) Let f : {1, 2, 3, 4…} → {1, 4, 9, 16…} be defined by f(x) = x2. Prove that the function is bijective.
— OR —
(b) Let f : R → R be defined by f(x) = x2. Show that f is neither injective nor surjective. |
[2] |