What is the inverse of f(x)=4arccos(1-2x)+pi/3 ?

The inverse of f(x)=4arccos(1-2x)+pi/3 is -(cos((3x-pi)/(12))-1)/2

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inverse of f(x)=4arccos(1-2x)+pi/3

inverse

f (x) = 4 arccos (1 - 2 x) + \frac{π}{3}

- \frac{cos ( \frac{3 x - π}{12} ) - 1}{2}

Solution steps

Solve for

arccos (1 - 2 x), y = 4 arccos (1 - 2 x) + \frac{π}{3}

arccos (1 - 2 x) = \frac{3 y - π}{12}

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

1 - 2 x = cos (\frac{3 y - π}{12})

Solve for

x, 1 - 2 x = cos (\frac{3 y - π}{12})

- \frac{cos ( \frac{3 y - π}{12} ) - 1}{2}

Substitute

y = x

- \frac{cos ( \frac{3 x - π}{12} ) - 1}{2}

3 x^{4}

f (x) = 3 (x + 5) 2 - 4

f (x) = - \frac{1}{5} x + 1

f (2) = - 9 x^{- 4}

f (x) = - \frac{2}{3} x - 24

What is the inverse of f(x)=4arccos(1-2x)+pi/3 ?
The inverse of f(x)=4arccos(1-2x)+pi/3 is -(cos((3x-pi)/(12))-1)/2