What is the domain of f(t)=tan(2t) ?

The domain of f(t)=tan(2t) is pi/2 n<= t< pi/4+pi/2 n\lor pi/4+pi/2 n<t< pi/2+pi/2 n

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domain of f(t)=tan(2t)

domain

f (t) = tan (2 t)

\frac{π}{2} n \leq t < \frac{π}{4} + \frac{π}{2} n or \frac{π}{4} + \frac{π}{2} n < t < \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

tan (2 t)

and compare to zero:

t = \frac{π}{4} + \frac{π}{2} n

Periodicity of

tan (2 t) : \frac{π}{2}

Combine period:

\frac{π}{2} n \leq t < \frac{π}{2} + \frac{π}{2} n

and undefined points.

The domain is

\frac{π}{2} n \leq t < \frac{π}{4} + \frac{π}{2} n or \frac{π}{4} + \frac{π}{2} n < t < \frac{π}{2} + \frac{π}{2} n

f (x) = \frac{3 x}{x - 7}

x + 9 - 7

f (x) = \frac{5 x - 14}{x - 3}

15 - x + 2

f (x) = 7 + 3 x - 6

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