Domainomania-2

Algebra Level 4

\[f(x)=\frac{1}{\lfloor |x-1| \rfloor + \lfloor |7-x|\rfloor-6}\] If the domain of above function is \((q,s] \cup \{a,b,c,d,e \}\cup [g,h)\), where \(q\), \(s\), \(a\), \(b\), \(c\), \(d\), \(e\), \(g\) and \(h\) are all integers.

Find \(q+s+a+b+c+d+e+g+h\).


Notations:

  • \(| \cdot |\) denotes the absolute value
  • \(\lfloor \cdot \rfloor\) denotes the floor function
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