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

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Answer 1 · 2018-07-30T14:22:35

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

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]}

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