CASE STUDY CHALLENGE

Relations & Functions: The Exhibition Swing

Rajesh, a student of Class-XII, visited an exhibition with his family. There he saw a huge swing and found that it traced the path of a parabola y = x2.

The following questions came to his mind. Answer the questions :

Answer the following:

(i) Let f : R → R be a function defined as f(x) = x2. Find whether f is one-one function. [1]
(ii) Let f : R → R be defined as f(x) = x2. Find whether f is an onto function. [1]
(iii) (a) Let f : N → N be defined as f(x) = x2. Find whether f is one-one function. Also, find if it is an onto function.

— OR —

(b) Let f : N → {1, 4, 9, 16, ……} defined as f(x) = x2, find where f is one-one function. Also, find if it is an onto function.

[2]