Question 1128484
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I will assume this question came from the same person whose similar question I just answered....<br>
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.<br>
So again I assume you mean f(g(x)) and g(f(x)).<br>
a) f(g(x)) can only exist for input values for which g(x) is defined: 2, 3, and 4.<br>
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<br>
So f(g(x)) = {(2,4), (3,3)}<br>
b) g(f(x)) can only exist for input values for which f(x) is defined: 1, 2, and 3.<br>
g(f(1)) = g(2) = 3  -->  (1,3)
g(f(2)) = g(3) = 2  -->  (2,2)
g(f(3)) = g(4) = 8  -->  (3,8)<br>
So g(f(x)) = {(1,3), (2,2), (3,8)}