What is the inverse of f(x)=sin((1-2x)/x) ?

The inverse of f(x)=sin((1-2x)/x) is 1/(2+arcsin(x))

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inverse of f(x)=sin((1-2x)/x)

inverse

f (x) = sin (\frac{1 - 2 x}{x})

\frac{1}{2 + arcsin ( x )}

Solution steps

sin (a) = b \Rightarrow a = arcsin (b)

\frac{1 - 2 x}{x} = arcsin (y)

Solve for

x, \frac{1 - 2 x}{x} = arcsin (y)

\frac{1}{2 + arcsin ( y )}

Substitute

y = x

\frac{1}{2 + arcsin ( x )}

What is the inverse of f(x)=sin((1-2x)/x) ?
The inverse of f(x)=sin((1-2x)/x) is 1/(2+arcsin(x))