Question

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 of f .​

Answer 1

Answer:

The functions f:{1 , 3 ,4} → {1 , 2 ,5} and g :{1 , 2 ,5 }→{1 , 3} are defined as

f:{(1 , 2) , (3 , 5) , (4 , 1)} and g :{(1 , 3) , (2 , 3) , (5 , 1)}

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

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

gof(4) = g(f(4)) =g(1) =3. [f(4) =1 and g(1)=3]

∴gof ={(1 , 3) , (3 , 1) , (4 , 3)}

Hope mah answer helped you..!!

Answer 2

ANSWER

The function f:1,3,5→1,2,5 and g:1,2,5→1,3 are defined as

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]

∴gof=(1,3),(3,1),(4,3)

$\huge \mathfrak \pink{hope \: it \: helps \: u}$