Let $f: N \rightarrow R$ be a function $f(n) = \lfloor{\frac{n}{2}} \rfloor$ prove that $f(n) \in \Theta (n)$

Question

Let $f: N \rightarrow R$ be a function $f(n) = \lfloor{\frac{n}{2}} \rfloor$. Prove that $f(n) \in \Theta (n)$

I came across this problem and honestly have no idea where to start.

Answer 1

For large enough $n$, $\dfrac{n}{3} \lt f(n) \le \dfrac{n}{2} $.

This should be enough.