Let `f: IvecI` be a function `(I` is set of integers`)` such that `f(0)=1,f(f(n)=f(f(n+2)+2)=ndot` then `f(3)=0` b. `f(2)=0` c. `f(3=-2)` d. `f` is many one function

Options

A. `f(3)=0`
B. `f(2)=0`
C. `f(3)=-2`
D. f is many -one function

Answer

C

Explanation

Given that `f(f(n)) = n and " (i)"`
f(0) = 1
Put n = 0, we get
`f(f(0))=0 or f(1)=0`
Also given that `f(f(n+2)+2)=n" (ii)"`
Put `n=-1`, we get
`f(f(1)+2)=-1 or f(0+2)=-1 or f(2)=-1`
For f(3), put n= -2 in (ii)
`therefore" "f(f(0)+2)=-2`
`"or "f(1+2)=-2`
`"or "f(3)=-2`