1.

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»

Given as f = {(1, −1), (4, −2), (9, −3), (16, 4)} and g = {(−1, −2), (−2, −4), (−3, −6), (4, 8)}

f: {1, 4, 9, 16} → {-1, -2, -3, 4} and g: {-1, -2, -3, 4} → {-2, -4, -6, 8}

Co-domain of f = domain of g

Therefore, gof exists and gof: {1, 4, 9, 16} → {-2, -4, -6, 8}

(gof)(1) = g(f(1)) = g(−1) = −2

(gof)(4) = g(f(4)) = g(−2) = −4

(gof)(9) = g(f(9)) = g(−3) = −6

(gof)(16) = g(f(16)) = g(4) = 8

Therefore, gof = {(1, −2), (4, −4), (9, −6), (16, 8)}

Since, the co-domain of g is not same as the domain of f.

Therefore, fog does not exist.


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