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

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

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Lecture 7 Part 2 Questions from Exercise 1.3, NCERT Exemplar, Boardâ€™s Question Bank

Revision of inverse functions (Invertible Functions)

**5.** Consider f : {1, 2, 3} â†’ {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 â†’ 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} â†’ {a, b, c} and g : {a, b, c} â†’ {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)