       Re: Solve and Piecewise Functions

• To: mathgroup at smc.vnet.net
• Subject: [mg76439] Re: Solve and Piecewise Functions
• From: Szabolcs <szhorvat at gmail.com>
• Date: Tue, 22 May 2007 02:51:49 -0400 (EDT)
• Organization: University of Bergen
• 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,x³4}}]
>   h=x-2;
>   Solve[g?h,x]
>
>
>   would give me a meaningful answer.  But all I get is this:
>
>
>   Solve[\[Piecewise]{
>   {0, x<0},
>   {2 x-x2, 0£x<4},
>   {16 x-x2, x³4}
>   }?-2+x,x]
>
>   Any thoughts on how to do this?
>

I don't think that Solve understands piecewise functions ...

You could use Solve separately for the three pieces, then pick those
solutions that satisfy the conditions.

In:= pwSolve[HoldPattern[Piecewise][pw_List, ___] == rhs_, x_] :=
With[{sol = Solve[#1 == rhs, x]}, Pick[sol, #2 /. sol]] & @@@ pw

In:= g =
Piecewise[{{0, x < 0}, {2 x - x^2, 0 <= x < 4}, {16 x - x^2,
x >= 4}}]

Out= \[Piecewise] {
{0, x < 0},
{2 x - x^2, 0 <= x < 4},
{16 x - x^2, x >= 4}
}

In:= h = x - 2

Out= -2 + x

In:= pwSolve[g == h, x]

Out= {{}, {{x -> 2}}, {{x -> 1/2 (15 + Sqrt)}}}

Note that this simple pwSolve ignores the default value of Piecewise ...

Szabolcs

```

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