Re: Determine the "value range" of a function

• To: mathgroup at smc.vnet.net
• Subject: [mg27184] Re: [mg27157] Determine the "value range" of a function
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Fri, 9 Feb 2001 03:10:29 -0500 (EST)
• References: <200102080940.EAA22644@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Dirk Heidenreich wrote:
>
> Hello,
>
> maybe its trivial but how can i determine the "value range" of a function?
> like  f(x)=Sin(x)     -> Range =-1..1
>
> Dirk Heidenreich

For simple cases, intervals can be used to this effect.

In[1]:= Sin[Interval[{-Infinity,Infinity}]]
Out[1]= Interval[{-1, 1}]

For, say, sums, you can get a superset of the actual range because the
intervals behave independently.

In[2]:= f[x_] := Sin[x] + Cos[x]

In[3]:= f[Interval[{-Infinity,Infinity}]]
Out[3]= Interval[{-2, 2}]

For functions that do not take on values in a continuum within the real
line, this method will not work at all.

Daniel Lichtblau
Wolfram Research

```

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