How do you find the domain and range of #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]}