Question

Find the domain of $f\left(x\right)=cotx+co{t}^{-1}x$

Answer 1

Solve for the required domain

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

The domain of the expression is all real numbers except where the expression is undefined.

$cotx$ is defined for $x\in R-\{n\pi ,n\in Z\}$

and $co{t}^{-1}x$ is defined for$x\in R$

Now we take the intersection of both domains $x\in R-\{n\pi ,n\in Z\}$ $\cap$$x\in R$

$\therefore$ domain for $f\left(x\right)$ is $R-\{n\pi ,\in Z\}$ ,$x\in R$

Hence the domain of $f\left(x\right)$ is $R-\{n\pi ,\in Z\}$