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

The domain of f(x)= 1/2 tan(3x) is pi/3 n<= x< pi/6+pi/3 n\lor pi/6+pi/3 n<x< pi/3+pi/3 n

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domain of f(x)= 1/2 tan(3x)

domain

f (x) = \frac{1}{2} tan (3 x)

\frac{π}{3} n \leq x < \frac{π}{6} + \frac{π}{3} n or \frac{π}{6} + \frac{π}{3} n < x < \frac{π}{3} + \frac{π}{3} n

Interval Notation

Solution steps

Take the denominator(s) of

\frac{1}{2} tan (3 x)

and compare to zero:

x = \frac{π}{6} + \frac{π}{3} n

Periodicity of

\frac{1}{2} tan (3 x) : \frac{π}{3}

Combine period:

\frac{π}{3} n \leq x < \frac{π}{3} + \frac{π}{3} n

and undefined points.

The domain is

\frac{π}{3} n \leq x < \frac{π}{6} + \frac{π}{3} n or \frac{π}{6} + \frac{π}{3} n < x < \frac{π}{3} + \frac{π}{3} n

f (x) = 2 ln (x - 1) + 1

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

lo g_{10} (x^{2} - 6 x + 9)

f (x) = 5 + 2 x

\frac{x - 7}{x ^{2} + 14 x + 49}

What is the domain of f(x)= 1/2 tan(3x) ?
The domain of f(x)= 1/2 tan(3x) is pi/3 n<= x< pi/6+pi/3 n\lor pi/6+pi/3 n<x< pi/3+pi/3 n