So here's the question:

Find f•g (relation) for each pair of functions f and g. Use understood domains for f and g.

a.) f(x)=2x+5, g(x)=6-7x

(f•g)(x)= 2(6-7x)+5 = 17-14x

(g•f)(x)= 6+7(2x+5) = -14x-29

Okay i understand this. But

b.) f(x)={(t,r),(s,r),(k,l)} , g(x)={(k,s),(t,s),(s,k)}

f•g = {(k,r),(t,r),(s,l)} but g•f=ø (null set)

i see how f•g works, replace the x value of f with the x value of g. But why is the relation of g•f the null set?

wouldnt it be {(t,s),(s,s),(k,k)}?

Now i see that t and s have the same y variable 's' which doesent make this a function.

BUT f(x) has t and s with the same value 'r' so its not a function in the first place right??

Please help a fellow understand. Pictures would be great.