Question

Mark the correct alternative in the following question:

Let f : R $\to$ R be given by f(x) = tanx. Then, f ^$-$1(1) is

(a) $\frac{\mathrm{\pi }}{4}$ (b) $\left\{n\mathrm{\pi }+\frac{\mathrm{\pi }}{4}:n\in \mathbf{Z}\right\}$ (c) does not exist (d) none of these

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ f:\mathbf{R}\to \mathbf{R}\mathrm{is}\mathrm{given}\mathrm{by} \\ f\left(x\right)=\tan x \\ \Rightarrow f^{-1}\left(x\right)={\tan }^{-1}x \\ \therefore f^{-1}\left(1\right)={\tan }^{-1}1=\left\{n\mathrm{\pi }+\frac{\mathrm{\pi }}{4}:n\in \mathbf{Z}\right\} \end{gathered}$$

Hence, the correct alternative is option (b).