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Re: Solve and Piecewise Functions


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[gÅ 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}
>   }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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