If `fa n dg` are two functions defined on `N ,` such that `f(n)-{2n-1ifni se v e n2n+2ifni sod d` and `g(n)=f(n)+f(n+1)dot` Then range of `g` is `{m in N : m=` multiple of 4`}` `{` set of even natural numbers`}` `{m in N : m=4k+3,k` is a natural number `{m in N : m=` multiple of 3 or multiple of 4`}`

Options

A. { m `in` N : m = multiple of 4}
B. { set of even natural numbers}
C. {m `in` N : m = 4k + 3, k is a natural number}
D. {m `in` N : m = multiple of 3 or multiple of 4}

Answer

C

Explanation

`g(n)=f(n)+f(n+1)`
If n is even, `n+1` is odd.
`therefore" "g(n)=2n-12(n+1)+2=4n+3`
If n is odd, `n+1` is even.
`therefore" "g(n)=2n+2+2(n+1)-1=4n+3.`