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

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

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

inverse

f (x) = 4 cos (1 - 2 x) + \frac{π}{3}

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

Solution steps

Solve for

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

cos (1 - 2 x) = \frac{3 y - π}{12}

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

1 - 2 x = arccos (\frac{3 y - π}{12})

Solve for

x, 1 - 2 x = arccos (\frac{3 y - π}{12})

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

Substitute

y = x

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

2 - 1

2 + x

f (x) = y^{2} = x - 5

f (x) = 2^{- x} + 3

2.1

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