Let N be the set of natural numbers and two functions f and g be defined as f, g: N → N such that f( n )= {(n +1)/2, if n is odd; n/2, if n is even}…

Let $\displaystyle \mathbf{N}$ be the set of natural numbers and two functions $\displaystyle f$ and $\displaystyle g$ be defined as $\displaystyle f, g: \mathbf{N} \rightarrow \mathbf{N}$ such that $$f(\mathrm{n})=\left\{\begin{array}{cl} \frac{\mathrm{n}+1}{2} & \text { if } \mathrm{n} \text { is odd } \\ \frac{\mathrm{n}}{2} & \text { if } \mathrm{n} \text { is even } \end{array}\right. $$ and $\displaystyle g(\mathbf{n})=\mathbf{n}-(-1)^{\mathbf{n}}$. Then $\displaystyle f \circ g$ is :