What is the domain of f(x)=4tan(2x+pi/3)-1 ?

The domain of f(x)=4tan(2x+pi/3)-1 is pi/2 n<= x< pi/(12)+pi/2 n\lor pi/(12)+pi/2 n<x< pi/2+pi/2 n

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domain of f(x)=4tan(2x+pi/3)-1

domain

f (x) = 4 tan (2 x + \frac{π}{3}) - 1

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

Interval Notation

Solution steps

Take the denominator(s) of

4 tan (2 x + \frac{π}{3}) - 1

and compare to zero:

x = \frac{π}{12} + \frac{π}{2} n

Periodicity of

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

f (x) = \frac{3 - x}{x + 5}

\frac{2}{x ^{2} - 2 x - 3}

\frac{2 x + 7}{x + 2}

f (x) = \frac{5}{x - 4} + x^{2} - 9

f (x) = x^{2} - 4, x \leq - 2

What is the domain of f(x)=4tan(2x+pi/3)-1 ?
The domain of f(x)=4tan(2x+pi/3)-1 is pi/2 n<= x< pi/(12)+pi/2 n\lor pi/(12)+pi/2 n<x< pi/2+pi/2 n