Let A a1 a2 and B b1 b2 b3 Let the function fA rightarrow

Let A = {a1, a2} and B = {b1, b2, b3}. Let the function f:A rightarrow B be given by the following set of ordered pairs: f= {(a1,b2),(a2,b3)}. List as a set of ordered pairs a function g with the property that for all a in A g(f(a)) = a, and show that this property holds.

Solution

in g(f(a)=a, we see that domain of function g is f

means domain of g contains range of f

which means domain of g is {b2,b3}

g(f(a)=a indicates range of g is same as domain of f means {a1,a2}

combining both results we get set of ordered pairs of g as

{(b2,a1),(b3,a2)}

Hence {(b2,a1),(b3,a2)} is the final answer .