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)

Algebra ->  Equations -> 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)      Log On


   

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) About Me  (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 y+=+abs%282x-4%29; I will guess that is what you are supposed to find here.

b) Each of the distinct points of g(x) satisfies the condition y+=+4-x; 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:

f%28g%28x%29%29+=+abs%282%284-x%29-4%29+=+abs%288-2x-4%29+=+abs%284-2x%29

And abs%284-2x%29 is the same as abs%282x-4%29