A function `f` from integers to integers is defined as
`f(n)={(n+3",",n in odd),(n//2 ",",n in even):}`
Suppose `k in odd and f(f(f(k)))=27.` Then the value of k is ________

Answer

105

Explanation

` :' k in odd`
`f(k)=k+3`
`f(f(x))=(k+3)/(2)`
If `(k+3)/(2)` is odd, then `27=(k+3)/(2)+3 or k=45` which is not possible.
Therefore,`(k+3)/(2)` is even. Thus,
`27=f(f(f(x)))=f((k+3)/(2))=(k+3)/(4)`
` :. k=105`
Verifying, `f(f(f(105)))=f(f(108))=f(54)=27`
` :. k=105`