function problem?

Question

Let A={2,4,6,8} , B={1,3,5,7}, C={a,b,c,d,e}, the function F:A->C be given 
by the rule F={(2,a),(4,b),(6,c),(8,d)} and the function g:B->A be given by 
the rule g={(1,2),(3,4),(5,6),(7,8)}

a) find f*g

b) is f onto? explain

c) is g onto? explain

Randy P · Accepted Answer

g = {(1,2), (3, 4), (5,6), (7,8) }.
f*g means replace the second number in each pair by f of that number. For instance in (1,2) you replace 2 by what f maps 2 to, which is a, since f contains the rule (2, a).

So the first pair in f*g is (1, a).
The second is (3, f(4))
And so on.

b) Does every element of C occur in f?
c) Does every element of A occur in g?

function problem?

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