What is the inverse of f(x)=sin(x^3) ?

The inverse of f(x)=sin(x^3) is cube root of arcsin(x)

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inverse of f(x)=sin(x^3)

inverse

f (x) = sin (x^{3})

3 arcsin (x)

Solution steps

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

x^{3} = arcsin (y)

Solve for

x, x^{3} = arcsin (y)

3 arcsin (y)

Substitute

y = x

3 arcsin (x)

f (x) = \frac{3 x}{1 - 2 x}

f (x) = (- 3.1)

f (x) = 5 x - 3 = 12

5 sin (x) + 2

f (x) = (\frac{1}{3}) x + 7

What is the inverse of f(x)=sin(x^3) ?
The inverse of f(x)=sin(x^3) is cube root of arcsin(x)