What is the domain of f(x)= 1/2 cot(x/2-(2pi)/3)-1 ?

The domain of f(x)= 1/2 cot(x/2-(2pi)/3)-1 is 2pin<= x<(4pi)/3+2pin\lor (4pi)/3+2pin<x<2pi+2pin

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domain of f(x)= 1/2 cot(x/2-(2pi)/3)-1

domain

f (x) = \frac{1}{2} cot (\frac{x}{2} - \frac{2 π}{3}) - 1

2 πn \leq x < \frac{4 π}{3} + 2 πn or \frac{4 π}{3} + 2 πn < x < 2 π + 2 πn

Interval Notation

[2 πn, \frac{4 π}{3} + 2 πn) \cup (\frac{4 π}{3} + 2 πn, 2 π + 2 πn)

Solution steps

Take the denominator(s) of

\frac{1}{2} cot (\frac{x}{2} - \frac{2 π}{3}) - 1

and compare to zero:

x = \frac{4 π}{3} + 2 πn

Periodicity of

\frac{1}{2} cot (\frac{x}{2} - \frac{2 π}{3}) - 1 : 2 π

Combine period:

2 πn \leq x < 2 π + 2 πn

and undefined points.

The domain is

2 πn \leq x < \frac{4 π}{3} + 2 πn or \frac{4 π}{3} + 2 πn < x < 2 π + 2 πn

f (x) = 16 x^{2}

x + 6 \cdot (x^{2} + 3)

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

f (x) = - 16 y^{2} + 8 y + 24

f (x) = \frac{3 ( x - 2 )}{x - 1}

What is the domain of f(x)= 1/2 cot(x/2-(2pi)/3)-1 ?
The domain of f(x)= 1/2 cot(x/2-(2pi)/3)-1 is 2pin<= x<(4pi)/3+2pin\lor (4pi)/3+2pin<x<2pi+2pin