What is the domain of tan(4t) ?

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

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domain of tan(4t)

domain

tan (4 t)

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

tan (4 t)

and compare to zero:

t = \frac{π}{8} + \frac{π}{4} n

Periodicity of

tan (4 t) : \frac{π}{4}

Combine period:

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

and undefined points.

The domain is

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

h (x) = x + 4

f (x) = 7 x + 8

y = 3^{x} - 1

f (z) = 3 z^{2} + 2 z - 4

f (x) = \frac{2 x}{∣ x ∣}

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