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.
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)}