Question

What is the domain of y=-tan^2(x) ?

Answer 1

`x ne ( 2 k + 1 ) pi/4, k = 0, +-1, +-2, +-3. ...`. See graph.

Explanation:

The asymptotes are x = zeros of the denominator `cos 2x`,

`x = ( 2 k + 1 ) pi / 4, k = 0, +-1, +-2, +-3. ...`
So, `x ne ( 2 k + 1 ) pi / 4, k = 0, +-1, +-2, +-3. ...`

graph{(x-pi/4+0.01y)(y-tan(2x)) =0[-4 4 -2 2]}

One asymptote `x = pi/4` is marked.

The space in between the asympyote and the nearby branch of the

graph `darr` as `abs y uarr` but never becomes 0. So this x is not

in the graph..