Given a function
F[x,y]=x+y
I want to find all values of y for which
Abs[F[x,y]]<= 5
when
0 <= x <= 1
The answer should be
0 <= y <= 4
Is there built in functionality that can handle a problem of this type? I'm looking for a shortcut to help avoid implementing a full blown algorithm on my own.
We may use
Reduce[Abs[x + y] <= 5 && 0 <= x <= 1, {y}, Reals]
which yields
0 <= x <= 1 && -5 - x <= y <= 5 - x
In fact the answer may not be 0<=y<=4 e.g. x = .5 and y = -2.5 gives Abs[x+y] = 2 <= 5