What is the inverse of f(x)=((-(cos(pi*y)-1))/2) ?

The inverse of f(x)=((-(cos(pi*y)-1))/2) is (arccos(-2y+1))/pi

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inverse of f(x)=((-(cos(pi*y)-1))/2)

inverse

f (x) = (\frac{- ( cos ( π \cdot y ) - 1 )}{2})

\frac{arccos ( - 2 y + 1 )}{π}

Solution steps

Solve for

cos (π \cdot y), x = \frac{- ( cos ( π \cdot y ) - 1 )}{2}

cos (π \cdot y) = - 2 x + 1

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

π y = arccos (- 2 x + 1)

Solve for

y, π \cdot y = arccos (- 2 x + 1)

\frac{arccos ( - 2 x + 1 )}{π}

Substitute

x = y

\frac{arccos ( - 2 y + 1 )}{π}

- 4 x - 3

- 4 x - 2

y = 11.25 x + 90

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

e^{x^{2} - 9}

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