What is the inverse of f(x)=-1/5 sin(x/3) ?

The inverse of f(x)=-1/5 sin(x/3) is 3arcsin(-5x)

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inverse of f(x)=-1/5 sin(x/3)

inverse

f (x) = - \frac{1}{5} sin (\frac{x}{3})

3 arcsin (- 5 x)

Solution steps

Solve for

sin (\frac{x}{3}), y = - \frac{1}{5} sin (\frac{x}{3})

sin (\frac{x}{3}) = - 5 y

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

\frac{x}{3} = arcsin (- 5 y)

Solve for

x, \frac{x}{3} = arcsin (- 5 y)

3 arcsin (- 5 y)

Substitute

y = x

3 arcsin (- 5 x)

\frac{x}{x - 2}

f (x) = 3 - 4 x + 2

7 x + 2

f (x) = 2 x^{2} + 16 x + 96

f (x) = 0.5 x + 3

What is the inverse of f(x)=-1/5 sin(x/3) ?
The inverse of f(x)=-1/5 sin(x/3) is 3arcsin(-5x)