# Part - 2 Lecture - 7 Chapter 1 Relations and Functions

Action is the foundational key to all success. – Pablo Picasso

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

Lecture 7 Part 2 Questions from Exercise 1.3, NCERT Exemplar, Board’s Question Bank

Revision of inverse functions (Invertible Functions)

5. Consider f : {1, 2, 3} → {a, b, c} given by f (1) = a, f (2) = b and f (3) = c. Find $$f^{-1}$$ and show that $$(f^{-1})^{-1}=f$$. (N)

6. Let f, g and h be functions from R to R. Show that (N)

$$(f+g)oh=foh+goh$$
$$(f.g)oh=(foh).(goh)$$

7. Let f: X → Y be an invertible function. Show that the inverse of $$f^{-1}$$ is f, i.e., $$(f^{-1})^{-1}=f$$. (N)

8. Consider f : {1, 2, 3} → {a, b, c} and g : {a, b, c} → {apple, ball, cat} defined as f(1) = a, f(2) = b, f(3) = c, g(a) = apple, g(b) = ball and g(c) = cat. Show that f, g and gof are invertible. Find out $$f^{-1},g^{-1}(gof)^{-1}$$ and show that $$(gof)^{-1}=f^{-1}og^{-1}$$. (N)