Answer
The domain includes all real numbers except those real numbers with the following form: $x = \frac{\pi}{4}+\frac{\pi~n}{2}$, where $n$ is an integer.
The range includes all real numbers.
Work Step by Step
$f(x) = -4~tan(2x+\pi)$
The domain includes all real numbers, except values of $x$ such that $2x+\pi = \frac{\pi}{2}+\pi~n$, where $n$ is an integer.
We can find an expression for these values of $x$:
$2x+\pi = \frac{\pi}{2}+\pi~n$, where $n$ is an integer.
$2x = \frac{\pi}{2}+\pi~n$, where $n$ is an integer.
$x = \frac{\pi}{4}+\frac{\pi~n}{2}$, where $n$ is an integer.
The domain includes all real numbers except those real numbers with the following form: $x = \frac{\pi}{4}+\frac{\pi~n}{2}$, where $n$ is an integer.
The range includes all real numbers.
