What is the domain of y=tan(2x-pi/3) ?

The domain of y=tan(2x-pi/3) is pi/2 n<= x<(5pi)/(12)+pi/2 n\lor (5pi)/(12)+pi/2 n<x< pi/2+pi/2 n

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domain of y=tan(2x-pi/3)

domain

y = tan (2 x - \frac{π}{3})

\frac{π}{2} n \leq x < \frac{5 π}{12} + \frac{π}{2} n or \frac{5 π}{12} + \frac{π}{2} n < x < \frac{π}{2} + \frac{π}{2} n

Interval Notation

[\frac{π}{2} n, \frac{5 π}{12} + \frac{π}{2} n) \cup (\frac{5 π}{12} + \frac{π}{2} n, \frac{π}{2} + \frac{π}{2} n)

Solution steps

Take the denominator(s) of

tan (2 x - \frac{π}{3})

and compare to zero:

x = \frac{5 π}{12} + \frac{π}{2} n

Periodicity of

tan (2 x - \frac{π}{3}) : \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{5 π}{12} + \frac{π}{2} n or \frac{5 π}{12} + \frac{π}{2} n < x < \frac{π}{2} + \frac{π}{2} n

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

7 - 6 cos (θ)

(- 5, 2), (- 2, 6)

f (x) = \frac{1}{3}

f (x) = x + 6 + 8 - x

What is the domain of y=tan(2x-pi/3) ?
The domain of y=tan(2x-pi/3) is pi/2 n<= x<(5pi)/(12)+pi/2 n\lor (5pi)/(12)+pi/2 n<x< pi/2+pi/2 n