What is the domain of 5tan(5x) ?

The domain of 5tan(5x) is pi/5 n<= x< pi/(10)+pi/5 n\lor pi/(10)+pi/5 n<x< pi/5+pi/5 n

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domain of 5tan(5x)

domain

5 tan (5 x)

\frac{π}{5} n \leq x < \frac{π}{10} + \frac{π}{5} n or \frac{π}{10} + \frac{π}{5} n < x < \frac{π}{5} + \frac{π}{5} n

Interval Notation

[\frac{π}{5} n, \frac{π}{10} + \frac{π}{5} n) \cup (\frac{π}{10} + \frac{π}{5} n, \frac{π}{5} + \frac{π}{5} n)

Solution steps

Take the denominator(s) of

5 tan (5 x)

and compare to zero:

x = \frac{π}{10} + \frac{π}{5} n

Periodicity of

5 tan (5 x) : \frac{π}{5}

Combine period:

\frac{π}{5} n \leq x < \frac{π}{5} + \frac{π}{5} n

and undefined points.

The domain is

\frac{π}{5} n \leq x < \frac{π}{10} + \frac{π}{5} n or \frac{π}{10} + \frac{π}{5} n < x < \frac{π}{5} + \frac{π}{5} n

What is the domain of 5tan(5x) ?
The domain of 5tan(5x) is pi/5 n<= x< pi/(10)+pi/5 n\lor pi/(10)+pi/5 n<x< pi/5+pi/5 n