What is the domain of f(x)=tan(3x) ?

The domain of f(x)=tan(3x) is pi/3 n<= x< pi/6+pi/3 n\lor pi/6+pi/3 n<x< pi/3+pi/3 n

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domain of f(x)=tan(3x)

domain

f (x) = tan (3 x)

\frac{π}{3} n \leq x < \frac{π}{6} + \frac{π}{3} n or \frac{π}{6} + \frac{π}{3} n < x < \frac{π}{3} + \frac{π}{3} n

Interval Notation

[\frac{π}{3} n, \frac{π}{6} + \frac{π}{3} n) \cup (\frac{π}{6} + \frac{π}{3} n, \frac{π}{3} + \frac{π}{3} n)

Solution steps

Take the denominator(s) of

tan (3 x)

and compare to zero:

x = \frac{π}{6} + \frac{π}{3} n

Periodicity of

tan (3 x) : \frac{π}{3}

Combine period:

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

and undefined points.

The domain is

\frac{π}{3} n \leq x < \frac{π}{6} + \frac{π}{3} n or \frac{π}{6} + \frac{π}{3} n < x < \frac{π}{3} + \frac{π}{3} n

What is the domain of f(x)=tan(3x) ?
The domain of f(x)=tan(3x) is pi/3 n<= x< pi/6+pi/3 n\lor pi/6+pi/3 n<x< pi/3+pi/3 n