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

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

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

inverse

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

tan (π x - \frac{π}{2}) c

Solution steps

Solve for

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

arctan (\frac{x}{c}) = π y - \frac{π}{2}

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

\frac{x}{c} = tan (π y - \frac{π}{2})

Solve for

x, \frac{x}{c} = tan (π y - \frac{π}{2})

tan (π y - \frac{π}{2}) c

Substitute

y = x

tan (π x - \frac{π}{2}) c

y = 4 x - 5

f (x) = x^{4} - 2 x^{2} + 8

s (t) = \frac{5 t}{sin ( t )}

ln (x - 5)

f (x) = \frac{3 x}{x ^{2} + 4}

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