What is the inverse of arcsin(2ln(x)-1) ?

The inverse of arcsin(2ln(x)-1) is e^{(sin(x)+1)/2}

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inverse of arcsin(2ln(x)-1)

inverse

arcsin (2 ln (x) - 1)

e^{\frac{s i n ( x ) + 1}{2}}

Solution steps

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

2 ln (x) - 1 = sin (y)

Solve for

x, 2 ln (x) - 1 = sin (y)

e^{\frac{s i n ( y ) + 1}{2}}

Substitute

y = x

e^{\frac{s i n ( x ) + 1}{2}}

What is the inverse of arcsin(2ln(x)-1) ?
The inverse of arcsin(2ln(x)-1) is e^{(sin(x)+1)/2}