What is the inverse of f(x)=sin(x^3+1) ?

The inverse of f(x)=sin(x^3+1) is cube root of arcsin(x)-1

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inverse of f(x)=sin(x^3+1)

inverse

f (x) = sin (x^{3} + 1)

Solution steps

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

x^{3} + 1 = arcsin (y)

Solve for

x, x^{3} + 1 = arcsin (y)

Substitute

y = x

f (x) = 4 (x - 3)^{2} - 1

f (x) = 7 (x - 3)

f (x) = 2 + 2 x + 2

f (x) = \frac{( 6 x + 2 )}{( 2 x + 3 )}

f (x) = x^{2} - 4, x < - 2

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