The function g(h) is defined for integers h such that if h is even, g(h) = h/2 and if h is odd, g(h) = h + 5. Given that g(g(g(g(g(h))))) = 19, how many possible values for h would satisfy this equation?  Choose the correct choice from the following:
A) 1 B) 5 C) 7 D) 8 E) 11
Let me define terms:   in g(h) = R   h is argument, R is result, g() is function,   in g(g(g(g(g(h))))), g1 is inner most, g5 is outermost for identification.   From definition of function g, we can deduce that:   If Result is even then two possibilities for argument = 1 Even 1 Odd   If Result is odd then one possibility for argument = 1 Even   Since final result = 19 = Odd   Possibilities:   g1:1 Even   g2: 1*(Even,Odd ) =1 Even 1 Odd   g3: 1*(Even,Odd) + 1 Even =2 Even 1 Odd   g4: 2*(Even, Odd) + 1 Even =3 Even 2 Odd   g5: 3*(Even, Odd) + 2 Even =5 Even 3 Odd = Total 8   Ans 8 it is!
<result>D</result>
The function g(h) is defined for integers h such that if h is even, g(h) = h/2 and if h is odd, g(h) = h + 5. Given that g(g(g(g(g(h))))) = 19, how many possible values for h would satisfy this equation?