The function g(a) is defined for integers a such that if a is even, g(a) = a/2 and if a is odd, g(a) = a + 5. Given that g(g(g(g(g(a))))) = 19, how many possible values for a would satisfy this equation?
Pick one.
A) 1
B) 5
C) 7
D) 8
E) 11

Rationale: let me define terms : in g ( a ) = r a is argument , r is result , g ( ) is function , in g ( g ( g ( g ( g ( a ) ) ) ) ) , g 1 is inner most , g 5 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 : g 1 : 1 even g 2 : 1 * ( even , odd ) = 1 even 1 odd g 3 : 1 * ( even , odd ) + 1 even = 2 even 1 odd g 4 : 2 * ( even , odd ) + 1 even = 3 even 2 odd g 5 : 3 * ( even , odd ) + 2 even = 5 even 3 odd = total 8 ans d it is !
Answer: D