Let f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3} be given by f = {(1, 2), (3, 5), (4, 1)} and g = {(1, 3), (2, 3), (5, 1)}. Write down gof

Solution:

A function is a process or a relation that associates each element 'a' of a non-empty set A, to a single element 'b' of another non-empty set B.

According to the given problem,

The functions f : {1, 3, 4} → {1, 2, 5} and

g : {1, 2, 5} → {1, 3} be given by

f = {(1, 2), (3, 5), (4, 1)}

and g = {(1, 3), (2, 3), (5, 1)}

gof (1) = g [f (1)]

= g (2) = 3 [as f (1) = 2 and g (2) = 3]

gof (3) = g [f (3)]

= g (5) = 1 [as f (3) = 5 and g (5) = 1]

gof (4) = g [f (4)]

= g (1) = 3 [as f (4) = 1 and g (1) = 3]

Therefore,

gof = {(1, 3), (3, 1), (4, 3)}

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NCERT Solutions for Class 12 Maths - Chapter 1 Exercise 1.3 Question 1

Let f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3} be given by f = {(1, 2), (3, 5), (4, 1)} and g = {(1, 3), (2, 3), (5, 1)}. Write down gof.

Summary:

For the given function f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3} be given by f = {(1, 2), (3, 5), (4, 1)} and g = {(1, 3), (2, 3), (5, 1)},gof = {(1, 3), (3, 1), (4, 3)}