Question 969381: I need help with this problem
Let f=(−1ˏ2)ˏ(0ˏ−2)g=(−1ˏ−3)ˏ(4ˏ1)ˏ(−4ˏ−3)
Find f+g and its domain
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! a good reference for what you are asking is here.
it took a while to find it, but i was able to get what i was looking for.
not all references talk about operations on functions when you are given sets of point pairs.
this one does.
good thing too because it clears up a very basic assumption regarding what's defined and what's not defined and whether you can add two functions together when one of the x values is defined and the other x value is not defined, as is the case with your problem.
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut30b_operations.htm
based on this reference, there is only one point pair that is in both sets.
that would be the point pair of (-1,2) in f and the point pair of (-1,-3) in g.
f+g would therefore be f(-1) + g(-1) which is equal to 2 - 3 which is equal to -1.
the point pair in f+g is therefore (-1,-1).
it's the only point pair that's in both functions and therefore the only point pair that is valid.
the domain of f+g is -1 only because the x value of -1 is the only x value that's in both sets.
read the reference and you'll see what i mean.
it's an excellent reference on the topic and you are well advised to read it and understand it.
in relation to your problem, the intersection of the sets is (-1) only and so your only domain in f+g is at x = -1 where you get f+g(-1) = -1 which results in the point pair of (-1,-1).
|
|
|
