SOLUTION: f(x)={(0,4),(1,2),(2,0),(3,2),(4,4)},g(x)={(0,4),(1,3),(2,2),(3,1),(4,0)} a) Find an expression for f(x) b) Find an expression for g(x) c) Find an expression for (f*g)(x)

Question 1128486: f(x)={(0,4),(1,2),(2,0),(3,2),(4,4)},g(x)={(0,4),(1,3),(2,2),(3,1),(4,0)}
a) Find an expression for f(x)
b) Find an expression for g(x)
c) Find an expression for (f*g)(x)
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

(1) I'm not sure what is meant by "find an expression for f(x)" when f(x) is defined as 5 distinct (x,y) values. So I will have to guess what the meaning is.

(2) "(f*g)(x)" is merely f(x)*g(x). In this problem that is not very interesting.

I very much suspect you mean "f(g(x))"; that function in this problem is quite interesting.

So I will guess that you meant f(g(x)).

a) Each of the distinct points of f(x) satisfies the condition ; I will guess that is what you are supposed to find here.

b) Each of the distinct points of g(x) satisfies the condition ; I will guess that is what you want here.

c) Assuming you mean f(g(x)), we can find f(g(x)) from the given function definitions.

f(g(0)) = f(4) = 4 --> (0,4)
f(g(1)) = f(3) = 2 --> (1,2)
f(g(2)) = f(2) = 0 --> (2,0)
f(g(3)) = f(1) = 2 --> (3,2)
f(g(4)) = f(0) = 4 --> (4,2)

From this we see that f(g(x)) is the same as f(x).

And we can see that algebraically:

And is the same as
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