What is the inverse of f(x)=arcsin(((2x-1))/3) ?

The inverse of f(x)=arcsin(((2x-1))/3) is (3sin(x)+1)/2

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inverse of f(x)=arcsin(((2x-1))/3)

inverse

f (x) = arcsin (\frac{( 2 x - 1 )}{3})

\frac{3 sin ( x ) + 1}{2}

Solution steps

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

\frac{2 x - 1}{3} = sin (y)

Solve for

x, \frac{2 x - 1}{3} = sin (y)

\frac{3 sin ( y ) + 1}{2}

Substitute

y = x

\frac{3 sin ( x ) + 1}{2}

f (x) = \frac{( x + 5 )}{x}

f (x) = 3 sin (x)

y = x^{9}

4 - x

9 x + 7

What is the inverse of f(x)=arcsin(((2x-1))/3) ?
The inverse of f(x)=arcsin(((2x-1))/3) is (3sin(x)+1)/2