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

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

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inverse of f(x)= 1/2 sin(2x-1)

inverse

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

\frac{arcsin ( 2 x ) + 1}{2}

Solution steps

Solve for

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

sin (2 x - 1) = 2 y

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

2 x - 1 = arcsin (2 y)

Solve for

x, 2 x - 1 = arcsin (2 y)

\frac{arcsin ( 2 y ) + 1}{2}

Substitute

y = x

\frac{arcsin ( 2 x ) + 1}{2}

f (x) = \frac{1}{2} x - 6

f (x) = \frac{2 x + 1}{x + 4}

x + 2 y = - 6

f (x) = 2 x y - 4 x + 6 y - 3 = 0

f (x) = 5 x - 10 y = 30

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