What is the domain of tan(pi/3 x) ?

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

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domain of tan(pi/3 x)

domain

tan (\frac{π}{3} x)

3 n \leq x < \frac{3}{2} + 3 n or \frac{3}{2} + 3 n < x < 3 + 3 n

Interval Notation

[3 n, \frac{3}{2} + 3 n) \cup (\frac{3}{2} + 3 n, 3 + 3 n)

Solution steps

Take the denominator(s) of

tan (\frac{π}{3} x)

and compare to zero:

x = \frac{3}{2} + 3 n

Periodicity of

tan (\frac{π}{3} x) : 3

Combine period:

3 n \leq x < 3 + 3 n

and undefined points.

The domain is

3 n \leq x < \frac{3}{2} + 3 n or \frac{3}{2} + 3 n < x < 3 + 3 n

d o main f (x) = \frac{x}{9 x + 5}

r an g e 2 x^{3} - x

in t erce pt s f (x) = 2 x^{2} + 4 x - 10

in v erse 5 x + 1 - 2

in v erse f (x) = lo g_{5} (\frac{( 1 - x )}{1 + x})

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