What is the domain of f(x)=tan(6x-4) ?

The domain of f(x)=tan(6x-4) is pi/6 n<= x<(8-pi)/(12)+pi/6 n\lor (8-pi)/(12)+pi/6 n<x< pi/6+pi/6 n

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domain of f(x)=tan(6x-4)

domain

f (x) = tan (6 x - 4)

\frac{π}{6} n \leq x < \frac{8 - π}{12} + \frac{π}{6} n or \frac{8 - π}{12} + \frac{π}{6} n < x < \frac{π}{6} + \frac{π}{6} n

Interval Notation

[\frac{π}{6} n, \frac{8 - π}{12} + \frac{π}{6} n) \cup (\frac{8 - π}{12} + \frac{π}{6} n, \frac{π}{6} + \frac{π}{6} n)

Solution steps

Take the denominator(s) of

tan (6 x - 4)

and compare to zero:

x = \frac{8 - π}{12} + \frac{π}{6} n

Periodicity of

tan (6 x - 4) : \frac{π}{6}

Combine period:

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

and undefined points.

The domain is

\frac{π}{6} n \leq x < \frac{8 - π}{12} + \frac{π}{6} n or \frac{8 - π}{12} + \frac{π}{6} n < x < \frac{π}{6} + \frac{π}{6} n

What is the domain of f(x)=tan(6x-4) ?
The domain of f(x)=tan(6x-4) is pi/6 n<= x<(8-pi)/(12)+pi/6 n\lor (8-pi)/(12)+pi/6 n<x< pi/6+pi/6 n