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

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

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

domain

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

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

Interval Notation

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

Solution steps

Take the denominator(s) of

cot (\frac{1}{3} (x - \frac{π}{2}))

and compare to zero:

x = \frac{π}{2} + 3 πn

Periodicity of

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

Combine period:

3 πn \leq x < 3 π + 3 πn

and undefined points.

The domain is

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

x^{2} + 6 x

x^{2} + 3 x

3^{x - 1}

f (x) = 4 x - 4

f (x) = tan (x) + cos (x)

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