What is the domain of f(x)=2cot(4x) ?

The domain of f(x)=2cot(4x) is pi/4 n<x< pi/4+pi/4 n

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domain of f(x)=2cot(4x)

domain

\frac{π}{4} n < x < \frac{π}{4} + \frac{π}{4} n

Interval Notation

(\frac{π}{4} n, \frac{π}{4} + \frac{π}{4} n)

Solution steps

Take the denominator(s) of

2 cot (4 x)

and compare to zero:

x = \frac{π}{4} n

Periodicity of

2 cot (4 x) : \frac{π}{4}

Combine period:

\frac{π}{4} n \leq x < \frac{π}{4} + \frac{π}{4} n

and undefined points.

The domain is

\frac{π}{4} n < x < \frac{π}{4} + \frac{π}{4} n

What is the domain of f(x)=2cot(4x) ?
The domain of f(x)=2cot(4x) is pi/4 n<x< pi/4+pi/4 n