What is the domain of 2/3 tan(2x+pi) ?

The domain of 2/3 tan(2x+pi) is pi/2 n<= x< pi/4+pi/2 n\lor pi/4+pi/2 n<x< pi/2+pi/2 n

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domain of 2/3 tan(2x+pi)

domain

\frac{2}{3} tan (2 x + π)

\frac{π}{2} n \leq x < \frac{π}{4} + \frac{π}{2} n or \frac{π}{4} + \frac{π}{2} n < x < \frac{π}{2} + \frac{π}{2} n

Interval Notation

Solution steps

Take the denominator(s) of

\frac{2}{3} tan (2 x + π)

and compare to zero:

x = \frac{π}{4} + \frac{π}{2} n

Periodicity of

\frac{2}{3} tan (2 x + π) : \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}{4} + \frac{π}{2} n or \frac{π}{4} + \frac{π}{2} n < x < \frac{π}{2} + \frac{π}{2} n

\frac{x ^{3} - 6 x ^{2} + 4 x + 8}{x ^{3} - x ^{2} - 9 x + 9}

y = \frac{x ^{2} - x}{x ^{2} - 1}

f (x) = \frac{3 x + 2}{x + 4}

f (x) = lo g_{10} (5) (3 x^{2} - 5 x + 2)

f (x) = \frac{1}{( x ^{2} - x )}

What is the domain of 2/3 tan(2x+pi) ?
The domain of 2/3 tan(2x+pi) is pi/2 n<= x< pi/4+pi/2 n\lor pi/4+pi/2 n<x< pi/2+pi/2 n