Question

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

Answer 1

Given $f\left(x\right)=co{s}^{-1}x$

The domain of $f\left(x\right)$ is equivalent to the range of values of $x$ for which $f\left(x\right)$ exists

Let $f\left(x\right)=\theta$ , we get $x=cos\theta$

The range of $cos\theta$ is $[-1,1]$

Therefore the range of $x$ is $[-1,1]$

Hence, the domain of $f\left(x\right)$ is $[-1,1]$