What is the inverse of f(x)=sin((1-3x)/x) ?

The inverse of f(x)=sin((1-3x)/x) is 1/(3+arcsin(x))

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inverse of f(x)=sin((1-3x)/x)

inverse

f (x) = sin (\frac{1 - 3 x}{x})

\frac{1}{3 + arcsin ( x )}

Solution steps

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

\frac{1 - 3 x}{x} = arcsin (y)

Solve for

x, \frac{1 - 3 x}{x} = arcsin (y)

\frac{1}{3 + arcsin ( y )}

Substitute

y = x

\frac{1}{3 + arcsin ( x )}

f (x) = 14 x

2 - x + 5

- 2 x - 1

\frac{2 x ^{2} + 5}{x ^{2} - 1}

f (x) = 2 x^{2} - 12 x + 13

What is the inverse of f(x)=sin((1-3x)/x) ?
The inverse of f(x)=sin((1-3x)/x) is 1/(3+arcsin(x))