# 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 â€“ {3} and B = R â€“ {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 \( f(x) = \frac{x}{x^2 + 1}, \forall x \in R \)Â