What is the inverse of f(x)=sin(ln(x^3-2)) ?

The inverse of f(x)=sin(ln(x^3-2)) is cube root of e^{arcsin(x)}+2

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inverse of f(x)=sin(ln(x^3-2))

inverse

3 e^{a r c s i n (x)} + 2

Solution steps

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

ln (x^{3} - 2) = arcsin (y)

Solve for

x, ln (x^{3} - 2) = arcsin (y)

3 e^{a r c s i n (y)} + 2

Substitute

y = x

3 e^{a r c s i n (x)} + 2

What is the inverse of f(x)=sin(ln(x^3-2)) ?
The inverse of f(x)=sin(ln(x^3-2)) is cube root of e^{arcsin(x)}+2