What is the inverse of f(x)=sqrt(e^{9sin(x))} ?

The inverse of f(x)=sqrt(e^{9sin(x))} is arcsin((2ln(x))/9)

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inverse of f(x)=sqrt(e^{9sin(x))}

inverse

f (x) = e^{9 s i n (x)}

arcsin (\frac{2 ln ( x )}{9})

Solution steps

Solve for

sin (x), y = e^{9 s i n (x)}

sin (x) = \frac{2 ln ( y )}{9}

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

arcsin (\frac{2 ln ( y )}{9})

Substitute

y = x

arcsin (\frac{2 ln ( x )}{9})

f (x) = \frac{- 5 x}{4} - 20

f (x) = x_{8}

3 \frac{x - 1}{3}

y = \frac{( - 1 ) 3 ^{x}}{11111111} + 12

f (t) = 100 (2^{\frac{t}{3}})

What is the inverse of f(x)=sqrt(e^{9sin(x))} ?
The inverse of f(x)=sqrt(e^{9sin(x))} is arcsin((2ln(x))/9)