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

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

domain

2 tan (2 x) + 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

2 tan (2 x) + 1

and compare to zero:

x = \frac{π}{4} + \frac{π}{2} n

Periodicity of

2 tan (2 x) + 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) = \frac{1 - ln ( x )}{1 - x ^{2}}

f (x) = \frac{10}{x ^{2} + 4}

f (x) = \frac{x ^{2} + x - 20}{x ^{2} - 14 x + 48}

\frac{2}{x + 7}

f (x) = lo g_{\frac{1}{2}} (lo g_{2} (x - 3))

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