What is the inverse of f(x)=(arccos(2x))/4+pi ?

The inverse of f(x)=(arccos(2x))/4+pi is (cos(4x-4pi))/2

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inverse of f(x)=(arccos(2x))/4+pi

inverse

f (x) = \frac{arccos ( 2 x )}{4} + π

\frac{cos ( 4 x - 4 π )}{2}

Solution steps

Solve for

arccos (2 x), y = \frac{arccos ( 2 x )}{4} + π

arccos (2 x) = 4 y - 4 π

arccos (a) = b \Rightarrow a = cos (b)

2 x = cos (4 y - 4 π)

Solve for

x, 2 x = cos (4 y - 4 π)

\frac{cos ( 4 y - 4 π )}{2}

Substitute

y = x

\frac{cos ( 4 x - 4 π )}{2}

y = - 23 x + 9

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

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

f (x) = \frac{7 x + 9}{x - 3}

40 x - 34 + (- 33) (1 - \frac{x}{0.4})^{2}

What is the inverse of f(x)=(arccos(2x))/4+pi ?
The inverse of f(x)=(arccos(2x))/4+pi is (cos(4x-4pi))/2