Question

What is the domain of `y=tan^3(x) +3`?

Answer 1

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

Explanation:

The period of `y = a tan^n(b x + c ) + d, n = 1, 2, 3, ...` is `pi/abs b` #.

The asymptotes are given by

`b x + c = ( 2 k + 1 ) pi/2 rArr x = 1/b ( ( 2 k + 1 ) pi/2 - c),`

`k = 0, +- 1, +- 2, +-3, ...`

So,

the period of `y = tan^3x + 3: pi`

The asymptotes: `x = ( 2k+ 1 ) pi/2, k = 0, +-1, +-2, +-3,...`

`rArr` the domain is given by

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

See graph, with asymptotes.
graph{(y - (tan(x ))^3 - 3 )(x-1/2pi+0.001y)=0}