Domain and range

*To*: mathgroup at smc.vnet.net*Subject*: [mg54063] Domain and range*From*: "DJ Craig" <spit at djtricities.com>*Date*: Wed, 9 Feb 2005 09:27:44 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

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.