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:

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

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