What is the inverse of f(x)=arctan(x^2-pi/4) ?

The inverse of f(x)=arctan(x^2-pi/4) is (sqrt(4tan(x)+pi))/2 ,-(sqrt(4tan(x)+pi))/2

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inverse of f(x)=arctan(x^2-pi/4)

inverse

f (x) = arctan (x^{2} - \frac{π}{4})

\frac{4 tan ( x ) + π}{2}, - \frac{4 tan ( x ) + π}{2}

Solution steps

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

x^{2} - \frac{π}{4} = tan (y)

Solve for

x, x^{2} - \frac{π}{4} = tan (y)

\frac{4 tan ( y ) + π}{2}, - \frac{4 tan ( y ) + π}{2}

Substitute

y = x

\frac{4 tan ( x ) + π}{2}, - \frac{4 tan ( x ) + π}{2}

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

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

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

f (x) = \frac{2}{5} x + 6

f (x) = \frac{8}{1 + x ^{2}}

What is the inverse of f(x)=arctan(x^2-pi/4) ?
The inverse of f(x)=arctan(x^2-pi/4) is (sqrt(4tan(x)+pi))/2 ,-(sqrt(4tan(x)+pi))/2