f, g and h are three functions defined from R to R as following:

(i) $f: R \rightarrow R$ such that $f(x)=x^{2}$

Since the value of x is squared, f(x) will always be equal or greater than 0.

$\therefore$ the range is $[0, \infty)$

(ii) $g: R \rightarrow R$ such that $g(x)=x^{2}+1$

Since, the value of $x$ is squared and also adding with $1, g(x)$ will always be equal or greater than 1 .

$\therefore$ Range of $g(x)=[1, \infty)$

(iii) $\mathrm{h}: \mathrm{R} \rightarrow \mathrm{R}$ such that $\mathrm{h}(\mathrm{x})=\sin \mathrm{x}$

We know that, $\sin (x)$ always lies between $-1$ to 1+

$\therefore$ Range of $h(x)=(-1,1)$