Question 1. If f : R \to A , given by f(x) = x^2 – 2x + 2 is onto functions, find set A.

Question 2. Is f : R \to R , given by f(x) = | x -1 | one – one? Give reason.

Question 3. f : R \to B , given by f(x) = sin x is onto function, then write the set B.

Question 4. Let A = R – {3} and B = R – {1}. Consider the function f : A \to B defined by f(x) = \left ( \frac{x-2}{x-3} \right) . Is f one-one and onto? Justify your answer.

Question 5. Check the following functions for one-one and onto:
a. f : R \to R, f(x) = \frac{2x – 3}{7}
b. f : R \to R, f(x) = | x + 1 |
c. f : R – {2} \to R, f(x) = \frac{3x – 1}{x – 2}

Question 6. Show that the function f : R \to R defined by f(x) = \frac{x}{x^2 + 1}, \forall x \in R