Consider the following two functions:

$f(n)=n^2*logn,g(n)=n^2*(logn-1)$

Which of the following statements is TRUE about the asymptotic relationships between these functions?

$g(n)$ is $(f(n))$ and $f(n)$ is $(g(n)),$ but $g(n)$ is not $O(f(n))$

$f(n)$ is $(g(n))$ and $f(n)$ is $(g(n)),$ but $g(n)$ is not $O(f(n))$

$g(n)$ is $(f(n))$ and $g(n)$ is $(f(n)),$ but $f(n)$ is not $O(g(n))$

$f(n)$ is $(g(n))$ and $g(n)$ is $(f(n)).$ but $f(n)$ is not $O(g(n))$