Question

How do you find the domain and range of `tan^-1(x)`?

Answer 1

The domain is `x in RR`. The range is `y in (-pi/2, pi/2)`

Explanation:

Before let's define the domain and range of

`y=tanx`

The domain of the function `y=tan x` is

`x in (-pi/2,pi/2)`

The range of the function `y=tan x` is

`y in (-oo, +oo)`

The function `y=tan^-1x` is symmetric to the function `y=tanx` with respect the line `y=x`

Therefore, the domain is `x in RR`

and the range is `y in (-pi/2, pi/2)`

graph{(y-tanx)(y-arctanx)(y-x)=0 [-5.014, 9.034, -3.367, 3.66]}