What is the domain of f(x)= 1/4 tan(4x) ?

The domain of f(x)= 1/4 tan(4x) is pi/4 n<= x< pi/8+pi/4 n\lor pi/8+pi/4 n<x< pi/4+pi/4 n

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domain of f(x)= 1/4 tan(4x)

domain

f (x) = \frac{1}{4} tan (4 x)

\frac{π}{4} n \leq x < \frac{π}{8} + \frac{π}{4} n or \frac{π}{8} + \frac{π}{4} n < x < \frac{π}{4} + \frac{π}{4} n

Interval Notation

[\frac{π}{4} n, \frac{π}{8} + \frac{π}{4} n) \cup (\frac{π}{8} + \frac{π}{4} n, \frac{π}{4} + \frac{π}{4} n)

Solution steps

Take the denominator(s) of

\frac{1}{4} tan (4 x)

and compare to zero:

x = \frac{π}{8} + \frac{π}{4} n

Periodicity of

\frac{1}{4} tan (4 x) : \frac{π}{4}

Combine period:

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

and undefined points.

The domain is

\frac{π}{4} n \leq x < \frac{π}{8} + \frac{π}{4} n or \frac{π}{8} + \frac{π}{4} n < x < \frac{π}{4} + \frac{π}{4} n

1 - cos (x)

y = 4 x - 2, (5, - 11)

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

y = \frac{2 x + 11}{3 x + 19}

f (x) = 13 x - 3

What is the domain of f(x)= 1/4 tan(4x) ?
The domain of f(x)= 1/4 tan(4x) is pi/4 n<= x< pi/8+pi/4 n\lor pi/8+pi/4 n<x< pi/4+pi/4 n