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Let f be the piecewise function such that

 

f(x) = { x2-5x-64 if x<=0,

         { x2-6x+10 if x>0

 

At how many points x does f(x)=2?

 

I got 2 before, but it says that I'm wrong. 

 May 5, 2019
 #1
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x2-5x-64=2 ⇒ x2-5x-66=0 ⇒ (x-11)(x+6)=0. x = -6 is the only negative solution.

 

x2-6x+10=2 ⇒ x2-6x+8=0 ⇒ (x-4)(x-2)=0.  x = 4 and x = 2 are both positive solutions.

 

Hence three solutions in total.

 May 5, 2019

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