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Composite Function

Let f :1,3,4→...

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 g o f .

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Solution

Given functions f:{ 1,3,4 }→{ 1,2,5 } and g:{ 1,2,5 }→{ 1,3 } are defined by f={ ( 1,2 ),( 3,5 ),( 4,1 ) } and g={ ( 1,3 ),( 2,3 ),( 5,1 ) } respectively.

We know that,

gof( 1 )=g( f( 1 ) ) =g( 2 ) =3

gof( 3 )=g( f( 3 ) ) =g( 5 ) =1

gof( 4 )=g( f( 4 ) ) =g( 1 ) =3

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

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Similar questions

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

f : {1, 3, 4} \to {1, 2, 5}

g : {1, 2, 5} \to {1, 3}

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

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

g o f

f : {1, 3, 4} \to {1, 2, 5}

g : {1, 2, 5} \to {1, 3}

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

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

g o f

\to

\to

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

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

f, g

h

R

R

(f + g) o h = f o h + g o h

(f . g) o h = (f o h) . (g o h)

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