If f : {5, 6} → {2, 3} and g : {2, 3} → {5, 6} are given by f = {(5, 2), (6, 3)} and g = {(2, 5), (3, 6)}, find fog.

Question

Philoid · Accepted Answer

Formula:-

(i)Let f : AB and g : BC be two functions.

Then, the composition of f and g, denoted by g o f, is defined as the function g o f : AC

given by g o f (x) = g (f (x))

Given:-

(i) f : {5, 6} → {2, 3}

(ii) g : {2, 3} → {5, 6}

(iv) f = {(5, 2), (6, 3)}

(v) g = {(2, 5), (3, 6)}

for fog(2)=f(g(2))

fog(2)=f(5)

fog(2)=2