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

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

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

inverse

f (x) = π - 3 \cdot arcsin (2 x - 1)

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

Solution steps

Solve for

arcsin (2 x - 1), y = π - 3 \cdot arcsin (2 x - 1)

arcsin (2 x - 1) = - \frac{y - π}{3}

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

2 x - 1 = sin (- \frac{y - π}{3})

Solve for

x, 2 x - 1 = sin (- \frac{y - π}{3})

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

Substitute

y = x

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

\frac{2 x - 3}{4 x + 1}

f (x) = x^{2} - x - 1

f (x) = 4 x - 12

f (x) = e^{9 x}

y = sin (8 x)

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