What is the inverse of f(x)= 1/2 arcsin(2x)+c ?

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

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inverse of f(x)= 1/2 arcsin(2x)+c

inverse

f (x) = \frac{1}{2} arcsin (2 x) + c

\frac{sin ( 2 x - 2 c )}{2}

Solution steps

Solve for

arcsin (2 x), y = \frac{1}{2} arcsin (2 x) + c

arcsin (2 x) = 2 y - 2 c

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

2 x = sin (2 y - 2 c)

Solve for

x, 2 x = sin (2 y - 2 c)

\frac{sin ( 2 y - 2 c )}{2}

Substitute

y = x

\frac{sin ( 2 x - 2 c )}{2}

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