What is the inverse of f(x)= 1/pi arctan(x)+1/2 ?

The inverse of f(x)= 1/pi arctan(x)+1/2 is tan(pix-pi/2)

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inverse of f(x)= 1/pi arctan(x)+1/2

inverse

f (x) = \frac{1}{π} arctan (x) + \frac{1}{2}

tan (π x - \frac{π}{2})

Solution steps

Solve for

arctan (x), y = \frac{1}{π} arctan (x) + \frac{1}{2}

arctan (x) = π y - \frac{π}{2}

arctan (a) = b \Rightarrow a = tan (b)

tan (π y - \frac{π}{2})

Substitute

y = x

tan (π x - \frac{π}{2})

What is the inverse of f(x)= 1/pi arctan(x)+1/2 ?
The inverse of f(x)= 1/pi arctan(x)+1/2 is tan(pix-pi/2)