# Part - 1 Lecture - 4 Chapter 1 Relations and Functions

“In the end, it’s not the years in your life that count. It’s the life in your years.” —*Abraham Lincoln*

Booklets/Notes/Assignments are typed here on this website and their PDFs will be made available soon.

**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