What is the inverse of f(x)=arcsin(e^x-2) ?

The inverse of f(x)=arcsin(e^x-2) is ln(sin(x)+2)

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inverse of f(x)=arcsin(e^x-2)

inverse

f (x) = arcsin (e^{x} - 2)

ln (sin (x) + 2)

Solution steps

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

e^{x} - 2 = sin (y)

Solve for

x, e^{x} - 2 = sin (y)

ln (sin (y) + 2)

Substitute

y = x

ln (sin (x) + 2)

f (x) = arcsin (1)

f (x) = \frac{3 x}{2 - x}

f (x) = 600 - 4 y

x^{2} + x + 1

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