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.
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.