What is the domain of 4tan(2x+pi)+1 ?

The domain of 4tan(2x+pi)+1 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 4tan(2x+pi)+1

domain

4 tan (2 x + π) + 1

\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

[\frac{π}{2} n, \frac{π}{4} + \frac{π}{2} n) \cup (\frac{π}{4} + \frac{π}{2} n, \frac{π}{2} + \frac{π}{2} n)

Solution steps

Take the denominator(s) of

4 tan (2 x + π) + 1

and compare to zero:

x = \frac{π}{4} + \frac{π}{2} n

Periodicity of

4 tan (2 x + π) + 1 : \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

f (x) = 3 x + x - 2

f (x) = - \frac{1}{81} x^{2} + 100

4 x - 2 y = 8

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

\frac{3 x}{2 - x}

What is the domain of 4tan(2x+pi)+1 ?
The domain of 4tan(2x+pi)+1 is pi/2 n<= x< pi/4+pi/2 n\lor pi/4+pi/2 n<x< pi/2+pi/2 n