What is the domain of 2tan(x/2) ?

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

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domain of 2tan(x/2)

domain

2 tan (\frac{x}{2})

2 πn \leq x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

Interval Notation

[2 πn, π + 2 πn) \cup (π + 2 πn, 2 π + 2 πn)

Solution steps

Take the denominator(s) of

2 tan (\frac{x}{2})

and compare to zero:

x = π + 2 πn

Periodicity of

2 tan (\frac{x}{2}) : 2 π

Combine period:

2 πn \leq x < 2 π + 2 πn

and undefined points.

The domain is

2 πn \leq x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

f (x) = 2 + 4 + 9 x

3 x - 3

f (x) = \frac{2 x - 6}{x - 1}

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

3 - lo g_{10} (x^{2} - 1)

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