${\text{f}}^{\text{'}}\left(\text{x}\right)=2-\text{cos x }\forall \text{x}\in \text{R⇒}$  one - one,

and ${\text{g}}^{\text{'}}\left(\text{x}\right)=\frac{1}{3}{\text{x}}^{-2/3}>0\Rightarrow$one - one

Since, both $\mathrm{g}$ and $\mathrm{f}$ are one - one, hence, $\mathrm{gof}$ is also one - one.

Range of $\mathrm{f}\left(\mathrm{x}\right)$ is $\left(-\mathrm{\infty },\mathrm{ }\mathrm{\infty }\right)$ as $\mathrm{f}\left(\mathrm{x}\right)$ is continuous and $\mathrm{f}\left(\mathrm{x}\right)\to \pm \mathrm{\infty }$ as $\mathrm{ }\mathrm{x}\to \pm \mathrm{\infty }$.

Also, since domain of $\mathrm{g}\left(\mathrm{x}\right)$ is $\mathrm{R}$, $\mathrm{y}={\mathrm{x}}^{\frac{1}{3}}$

$\Rightarrow \mathrm{x}={\mathrm{y}}^3$

$\Rightarrow {\mathrm{y}}^3\in \left(-\mathrm{\infty },\mathrm{ }\mathrm{\infty }\right)$

$\Rightarrow \mathrm{y}\in \left(-\mathrm{\infty },\mathrm{ }\mathrm{\infty }\right)$

$\Rightarrow$ Range of $\mathrm{g}\left(\mathrm{x}\right)$ is also $\mathrm{R}$.