What is the domain of y=tan(x/3) ?

The domain of y=tan(x/3) is 3pin<= x<(3pi)/2+3pin\lor (3pi)/2+3pin<x<3pi+3pin

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domain of y=tan(x/3)

domain

y = tan (\frac{x}{3})

3 πn \leq x < \frac{3 π}{2} + 3 πn or \frac{3 π}{2} + 3 πn < x < 3 π + 3 πn

Interval Notation

[3 πn, \frac{3 π}{2} + 3 πn) \cup (\frac{3 π}{2} + 3 πn, 3 π + 3 πn)

Solution steps

Take the denominator(s) of

tan (\frac{x}{3})

and compare to zero:

x = \frac{3 π}{2} + 3 πn

Periodicity of

tan (\frac{x}{3}) : 3 π

Combine period:

3 πn \leq x < 3 π + 3 πn

and undefined points.

The domain is

3 πn \leq x < \frac{3 π}{2} + 3 πn or \frac{3 π}{2} + 3 πn < x < 3 π + 3 πn

f (x) = ln (3 - 2 x^{2})

cos (5 x)

f (x) = - 2 x^{2} + 2 x + 82

- \frac{1}{x - 1}

(2, - 1), (3, 4)

What is the domain of y=tan(x/3) ?
The domain of y=tan(x/3) is 3pin<= x<(3pi)/2+3pin\lor (3pi)/2+3pin<x<3pi+3pin