What is the inverse of f(x)=sqrt(e^{3sin(x))} ?

The inverse of f(x)=sqrt(e^{3sin(x))} is arcsin((2ln(x))/3)

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inverse of f(x)=sqrt(e^{3sin(x))}

inverse

f (x) = e^{3 s i n (x)}

arcsin (\frac{2 ln ( x )}{3})

Solution steps

Solve for

sin (x), y = e^{3 s i n (x)}

sin (x) = \frac{2 ln ( y )}{3}

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

arcsin (\frac{2 ln ( y )}{3})

Substitute

y = x

arcsin (\frac{2 ln ( x )}{3})

What is the inverse of f(x)=sqrt(e^{3sin(x))} ?
The inverse of f(x)=sqrt(e^{3sin(x))} is arcsin((2ln(x))/3)