Question 41188: How do I solve the below equation? I know I have to add the two absolute value equations, but can not find any information on how to add them.
If f(x) = | x + 2| and g(x) = | x - 3 |, then (f + g)(x) =
Answer by zeynep(43)   (Show Source):
You can put this solution on YOUR website!
f(x) = x+2, if x>=-2
f(x) =-x-2, if x<-2
and
g(x) = x-3 , if x>=3
g(x) = -x+3, if x<3
to write (f+g)(x), we take the intersection of the domains of these two functions.
(f+g)(x)= (-x-2)+(-x+3), if x<-2
(f+g)(x)= (x+2)+(-x+3), if -2<=x<3
(f+g)(x)= (x+2)+(x-3), if x>=3
if we do these additions;
(f+g)(x)= -2x+1, if x<-2
(f+g)(x)= 5 , if -2<=x<3
(f+g)(x)= 2x-1, if x>=3
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