What is the inverse of f(x)=sqrt(e^{5sin(x))} ?

The inverse of f(x)=sqrt(e^{5sin(x))} is arcsin((2ln(x))/5)

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inverse of f(x)=sqrt(e^{5sin(x))}

inverse

f (x) = e^{5 s i n (x)}

arcsin (\frac{2 ln ( x )}{5})

Solution steps

Solve for

sin (x), y = e^{5 s i n (x)}

sin (x) = \frac{2 ln ( y )}{5}

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

arcsin (\frac{2 ln ( y )}{5})

Substitute

y = x

arcsin (\frac{2 ln ( x )}{5})

What is the inverse of f(x)=sqrt(e^{5sin(x))} ?
The inverse of f(x)=sqrt(e^{5sin(x))} is arcsin((2ln(x))/5)