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

1 Answer
Nov 8, 2017

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

Explanation:

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)