MathGroup Archive 2005

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Domain and range


How can I make Mathematica give me either a list or an inequality
representing all real values of x that will make f[x] either undefined,
imaginary, or infinite?  For example, if f[x] := (2x^2-18)/(x+3) then x
!= {-3}.  (-3 would give a 0 in the denominator)
Secondly, how can I find all real numbers that CANNOT be returned by
f[x] for any real, finite value of x.  In the example, f[x] != {-12}.

As a second example, ArcSin[x] only returns a real, finite number when
-1 <= x <= 1.  When it is passed a real, finite number, it can only
return values where -pi/2 <= ArcSin[x] <= pi/2.


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