What is the domain of tan(pi/8 x) ?

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

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domain of tan(pi/8 x)

domain

tan (\frac{π}{8} x)

8 n \leq x < 4 + 8 n or 4 + 8 n < x < 8 + 8 n

Interval Notation

[8 n, 4 + 8 n) \cup (4 + 8 n, 8 + 8 n)

Solution steps

Take the denominator(s) of

tan (\frac{π}{8} x)

and compare to zero:

x = 4 + 8 n

Periodicity of

tan (\frac{π}{8} x) : 8

Combine period:

8 n \leq x < 8 + 8 n

and undefined points.

The domain is

8 n \leq x < 4 + 8 n or 4 + 8 n < x < 8 + 8 n

cr i t i c a l h (x) = x^{2} + 4

s l o p e in t erce pt 2 x + y = 1

p a r i t y tan (2 x - 5)

r an g e f (x) = - 25 x^{2} - 10 x - 1

a sy m pt o t es f (x) = \frac{- 2 x}{x + 1}

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