Question

Write the domain of $f\left(x\right)={\sec }^{-1}x$.

Answer 1

Here, $F\left(x\right)=y={\sec }^{-1}x$

So, $x=\sec y$

now the Range of $\sec y$ is domain of ${\sec }^{-1}x$

i.e $\sec y$ is possible in

$R-(-1,1)$ So the Range

of $\sec y$ is $R-(-1,1)$ .. And

domain of $F\left(x\right)={\sec }^{-1}x$ is

$R-(-1,1)$

or we can say Domain of $F\left(x\right)=$

${\sec }^{-1}$ is $(-\infty ,-1]$ $U[1,\infty )$