Question $20$

Additional Points $-5($ this score will be adjusted manually$).$

Consider the following two functions:

$f(n)=n^2**sin(n)g(n)=n^2**(1+\frac{1}{n})$

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 $(f(n))$

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

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

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