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

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

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

domain

f (x) = cot (\frac{π}{3} + 2 x)

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

Interval Notation

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

Solution steps

Take the denominator(s) of

cot (\frac{π}{3} + 2 x)

and compare to zero:

x = \frac{π}{3} + \frac{π}{2} n

Periodicity of

cot (\frac{π}{3} + 2 x) : \frac{π}{2}

Combine period:

\frac{π}{2} n \leq x < \frac{π}{2} + \frac{π}{2} n

and undefined points.

The domain is

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

f (x) = sin (x) - x

3 x + 12

3 x + 10

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

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

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