• # question_answer Let $f:\,R\to R$ be defined by $f(x)=2x+\sin \,x$for $x\,\in R$. Then, $f$ is A)  one-one and onto                       B)  one-one but not onto C)  onto but not one-one                    D)  neither one-one nor onto

We have, $\tan \theta =\frac{r}{h/2}$ $\theta ={{45}^{o}},$ for all $r=\frac{h}{2}$ $\theta ={{45}^{o}}$         $n'=\frac{v}{v-{{v}_{s}}}\times n$ is strictly increasing. $\Rightarrow$            $\frac{n'}{n}=\frac{v}{v-{{v}_{s}}}$ is one-one