What is the domain of f(x)=cot(x+pi/6) ?

The domain of f(x)=cot(x+pi/6) is pin<= x<(5pi)/6+pin\lor pi-pi/6+pin<x<pi+pin

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domain of f(x)=cot(x+pi/6)

domain

f (x) = cot (x + \frac{π}{6})

πn \leq x < \frac{5 π}{6} + πn or π - \frac{π}{6} + πn < x < π + πn

Interval Notation

[πn, \frac{5 π}{6} + πn) \cup (π - \frac{π}{6} + πn, π + πn)

Solution steps

Take the denominator(s) of

cot (x + \frac{π}{6})

and compare to zero:

x = \frac{5 π}{6} + πn, x = π - \frac{π}{6} + πn

Periodicity of

cot (x + \frac{π}{6}) : π

Combine period:

πn \leq x < π + πn

and undefined points.

The domain is

πn \leq x < \frac{5 π}{6} + πn or π - \frac{π}{6} + πn < x < π + πn

f (x) = - 4 x + 5 + \frac{1}{5 x ^{2} + 2}

\frac{4}{( x - 7 ) ^{2}}

9 \cdot \frac{2}{3} + 5

f (t) = ln (2 t + 5)

f (x) = \frac{1}{2} sin (\frac{1}{2}) (x + \frac{π}{4})

What is the domain of f(x)=cot(x+pi/6) ?
The domain of f(x)=cot(x+pi/6) is pin<= x<(5pi)/6+pin\lor pi-pi/6+pin<x<pi+pin