How do you write the equation for the inverse of the function #y=pi/4+sin x#?

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Answer 1 · 2017-11-08T10:56:05

#f^-1(x)=arcsin(x-pi/4)#

To find the inverse function we have to express #y=pi/4+sinx# as a function of y:

#y=pi/4+sinx#

Multiply through by 4:

#4y=pi+4sinx#

Subtract #pi#

#4y-pi=4sinx#

Divide by 4:

#y-pi/4=sinx#

#x=arcsin(sinx)= arcsin(y-pi/4)#

Substituting y = x:

#arcsin(x-pi/4)#

So:

#f^-1(x)=arcsin(x-pi/4)#