How do you find the inverse of #y = Arctan(x+pi/2)#?

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Answer 1 · 2018-04-03T18:18:18

#f^-1(x)=tan(x)-pi/2#

To find the inverse we need to express #x# as a function of #y#

#y=arctan(x+pi/2)#

#tan(y)=tan(tarctan(x+pi/2))=x+pi/2#

#tany-pi/2=x#

Substituting:

#y=x#

#tan(x)-pi/2=y#

#f^-1(x)=tan(x)-pi/2#