# How do you find the domain & range for f(x)=sqrt(tan(2x+π))?

The range is (- $\infty$ , $\infty$ ) and domain is (- $\frac{\pi}{2}$ , $\frac{\pi}{4}$ )
Y = sqrt tan(2x + $\pi$) $\implies$ 0 < tan (2x + $\pi$ ) < $\infty$ $\implies$
0 < 2x + $\pi$ <$\frac{\pi}{2}$ $\implies$ -$\pi$ < 2x < - $\pi$ + $\frac{\pi}{2}$ $\implies$ -$\pi$ < 2x <$- \frac{\pi}{2}$ $\implies$
-$\frac{\pi}{2}$ < x < -$\frac{\pi}{4}$