Question

12. Let f = {(1, 2), (3, 4), (2, 2)) and g = {(2, 1), (3, 1), (4, 2)}. Find gof and fog.​

Answer 1

Answer :

• gof = { (1 , 1) , (2 , 1) , (3 , 2) }

• fog = { (2 , 2) , (3 , 3) , (4 , 3) }

Solution :

→ Given :

• f = { (1 , 2) , (3 , 4) , (2 , 2) }

• g = { (2 , 1) , (3 , 1) , (4 , 2) }

→ To find :

• gof = ?

• fog = ?

Now ,

We have , f = { (1 , 2) , (3 , 4) , (2 , 2) }

Thus ,

• f(1) = 2

• f(2) = 2

• f(3) = 4

Also ,

We have , g = { (2 , 1) , (3 , 1) , (4 , 2) }

• g(2) = 1

• g(3) = 1

• g(4) = 2

Now ,

We know that , (gof)(x) = g{f(x)}

Thus ,

• (gof)(1) = g{f(1)} = g(2) = 1

• (gof)(2) = g{f(2)} = g(2) = 1

• (gof)(3) = g{f(3)} = g(4) = 2

Thus ,

→ gof = { (1 , 1) , (2 , 1) , (3 , 2) }

Also ,

We know that , (fog)(x) = f{g(x)}

Thus ,

• (fog)(2) = f{g(2)} = f(1) = 2

• (fog)(3) = f{g(3)} = f(1) = 2

• (fog)(4) = f{g(4)} = f(2) = 2

Thus ,

→ fog = { (2 , 2) , (3 , 3) , (4 , 3) }

Hence ,

• gof = { (1 , 1) , (2 , 1) , (3 , 2) }

• fog = { (2 , 2) , (3 , 3) , (4 , 3) }