Q. 35.0( 2 Votes )

Let f = {(1, – 1), (4, – 2), (9, – 3), (16, 4)} and g = {(– 1, – 2), (– 2, – 4), (– 3, – 6), (4, 8)}. Show that gof is defined while fog is not defined. Also, find gof.

Answer :

We have,


f = {(1, – 1), (4, – 2) , (9, – 3), (16,4)} and


g = {(– 1, – 2), (– 2, – 4), (– 3, – 6), (4,8)}


Now,


Domain of f = {1,4,9,16}


Range of f = {– 1, – 2, – 3, 4}


Domain of g = (– 1, – 2, – 3,4}


Range of g = (– 2, – 4, – 6, 8}


Clearly range of f = domain of g


gof is defined.


but, range of g ≠ domain of f
So, fog is not defined.


Now,


gof(1) = g(– 1)= – 2


gof(4) = g(– 2) = – 4


gof(9) = g (– 3) = – 6


gof(16) = g(4)= 8


So, gof = {(1, – 2), (4, – 4), (9 , – 6), (16,8)}


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