Re: Solve and Piecewise Functions

• To: mathgroup at smc.vnet.net
• Subject: [mg76435] Re: Solve and Piecewise Functions
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Tue, 22 May 2007 02:49:44 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <f2rqtl\$9u1\$1@smc.vnet.net>

```Michael Madrid wrote:
> I was hoping something like this:
>
>
>   Clear["*"]
>   g=Piecewise[{{0,x<0},{2 x-x^2,0<=x<4},{16 x-x^2,xÂ³4}}]
>   h=x-2;
>   Solve[gÅ h,x]
>
>
>   would give me a meaningful answer.  But all I get is this:
>
>
>   Solve[\[Piecewise]{
>   {0, x<0},
>   {2 x-x2, 0Â£x<4},
>   {16 x-x2, xÂ³4}
>   }Å -2+x,x]
>
>   Any thoughts on how to do this?
>

Use Reduce rather than Solve.

In[1]:=
Clear["Global`*"]
g[x_] = Piecewise[{{0, x < 0}, {2*x - x^2,
Inequality[0, LessEqual, x, Less, 4]}},
16*x - x^2];
h[x_] = x - 2;
Reduce[g[x] == h[x], x]

Out[4]=
x == 2 || x == (1/2)*(15 + Sqrt[233])

Regards,
Jean-Marc

```

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