Question 1128484: f={(1,2),(2.3),(3,4)},g={(2,3),(3,2),(4,8)}
a) Find (f*g)(x)=
b) Find (g*f)(x)=
Answer by greenestamps(13334)   (Show Source):
You can put this solution on YOUR website!
I will assume this question came from the same person whose similar question I just answered....
Again, "(f*g)(x)" is simply f(x)*g(x); "(g*f)(x)" is simply g(x)*f(x). So the answers to the two questions would be the same.
So again I assume you mean f(g(x)) and g(f(x)).
a) f(g(x)) can only exist for input values for which g(x) is defined: 2, 3, and 4.
f(g(2)) = f(3) = 4 --> (2,4)
f(g(3)) = f(2) = 3 --> (3,3)
f(g(4)) = f(8) but f(8) is not defined
So f(g(x)) = {(2,4), (3,3)}
b) g(f(x)) can only exist for input values for which f(x) is defined: 1, 2, and 3.
g(f(1)) = g(2) = 3 --> (1,3)
g(f(2)) = g(3) = 2 --> (2,2)
g(f(3)) = g(4) = 8 --> (3,8)
So g(f(x)) = {(1,3), (2,2), (3,8)}
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