Question:

$f(x)=\cot^{-1}\left(\dfrac{x+1}{x}\right)$ is defined for all real $x$ except

$x=0$ only

$x=1$ only

$x\in[-1,1]$

$x\in[0,1]$

Step-by-Step Solution

Key Concept: $\cot^{-1}$ is defined for all real, so domain excludes only where argument is undefined

Defined for all $x\ne 0$.

Correct Answer: 4