Let the functions f AB and g BC be defined by f aybxcy g xsy

Let the functions f: A->B and g: B->C be defined by:

f: {(a,y),(b,x),(c,y)}

g: {(x,s),(y,t),(z,r)}

a. Find the composition function g o f : A->C

b. Find the ranges of f, g and g o f

Solution

a) the composition function g o f = {(x,x),(y,y)}

b) the range of f={y,x}

the range of g={s,t,r}

the range of g o f ={x,y}