A function f from integers to integers is defined as f(x)=n+3,n∈oddn2,n∈even   Suppose k∈ odd and f(f(f(k)))=27, then the sum of digits of k is

∵k∈odd  f(x)=k+3  f(f(k))=k+32  Ifk+32∈odd⇒27=k+32+3  k=45 not possible.Now,letk+32∈even∴ 27=f(f(f(k)))=f(k+32)=k+34∴ k=105verifying f(f(f(105)))=f(f(108))=f(54)=27∴k=105Hence, sum of digits of k = 1 + 0 +5 = 6