Question

The range of ${\sec }^{-1}x$ is

Answer 1

Range of ${\sec }^{-1}x$

Let,

$$\begin{gathered} y={\sec }^{-1}x \\ \Rightarrow \sec y=x \end{gathered}$$

Domain includes all numbers from $-\infty$ to $\infty$ except the numbers that are between $-1$ and $1$.

Thus, range of ${\sec }^{-1}x$ is all the angles that are between $0°$ and $180°$ expect $90°$.

Hence, the range is $\left[0,\mathrm{\pi }\right]-\left[\frac{\mathrm{\pi }}{2}\right]$.