What is the inverse of f(x)= 5/4 cos(4x+pi/2) ?

The inverse of f(x)= 5/4 cos(4x+pi/2) is (2arccos((4x)/5)-pi)/(8)

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inverse of f(x)= 5/4 cos(4x+pi/2)

inverse

f (x) = \frac{5}{4} cos (4 x + \frac{π}{2})

\frac{2 arccos ( \frac{4 x}{5} ) - π}{8}

Solution steps

Solve for

cos (4 x + \frac{π}{2}), y = \frac{5}{4} cos (4 x + \frac{π}{2})

cos (4 x + \frac{π}{2}) = \frac{4 y}{5}

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

4 x + \frac{π}{2} = arccos (\frac{4 y}{5})

Solve for

x, 4 x + \frac{π}{2} = arccos (\frac{4 y}{5})

\frac{2 arccos ( \frac{4 y}{5} ) - π}{8}

Substitute

y = x

\frac{2 arccos ( \frac{4 x}{5} ) - π}{8}

f (x) = \frac{2 x}{8 - x}

f (x) = 5 x (4 - x)

- 2^{x}

f (x) = \frac{( x - 1 ) ^{3}}{2} - 3

What is the inverse of f(x)= 5/4 cos(4x+pi/2) ?
The inverse of f(x)= 5/4 cos(4x+pi/2) is (2arccos((4x)/5)-pi)/(8)